Match each equation below with its solution(s) $$ \begin{array}{ll} ext { 1. } x^{2}=25 & ext { 2. } x^{2}=-25 \ \begin{array}{ll} ext { 3. } x^{2}+5=0 & ext { 4. } x^{2}-5=0 \ ext { 5. } x^{2}=-45 & ext { 6. } x^{2}=45 \ ext { 7. } x-5=0 & ext { 8. } x+5=0\end{array} \ \begin{array}{lll} \pm i \sqrt{5} & \pm 5 i & -5 \ 5 & \pm 3 i \sqrt{5} & \pm 3 \sqrt{5}\end{array}\end{array} $$

Question

Match each equation below with its solution(s) $$ \begin{array}{ll}	ext { 1. } x^{2}=25 & 	ext { 2. } x^{2}=-25 \ \begin{array}{ll}	ext { 3. } x^{2}+5=0 & 	ext { 4. } x^{2}-5=0 \ 	ext { 5. } x^{2}=-45 & 	ext { 6. } x^{2}=45 \ 	ext { 7. } x-5=0 & 	ext { 8. } x+5=0\end{array} \ \begin{array}{lll} \pm i \sqrt{5} & \pm 5 i & -5 \ 5 & \pm 3 i \sqrt{5} & \pm 3 \sqrt{5}\end{array}\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x+5=0$$
- step1: Move the constant to the right side:
  $$x=0-5$$
- step2: Remove 0:
  $$x=-5$$
Solve the equation $$ x-5=0 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x-5=0$$
- step1: Move the constant to the right side:
  $$x=0+5$$
- step2: Remove 0:
  $$x=5$$
Solve the equation $$ x^{2}=25 $$.
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
  $$x^{2}=25$$
- step1: Simplify the expression:
  $$x=\pm \sqrt{25}$$
- step2: Simplify the expression:
  $$x=\pm 5$$
- step3: Separate into possible cases:
  $$\begin{align}&x=5\&x=-5\end{align}$$
- step4: Rewrite:
  $$x_{1}=-5,x_{2}=5$$
Solve the equation $$ x^{2}=-25 $$.
Solve the equation(The complex numbers system) by following steps:
- step0: Solve using square roots:
  $$x^{2}=-25$$
- step1: Simplify the expression:
  $$x=\pm \sqrt{-25}$$
- step2: Simplify the expression:
  $$x=\pm 5i$$
- step3: Separate into possible cases:
  $$\begin{align}&x=5i\&x=-5i\end{align}$$
- step4: Rewrite:
  $$x_{1}=-5i,x_{2}=5i$$
Solve the equation $$ x^{2}+5=0 $$.
Solve the equation(The complex numbers system) by following steps:
- step0: Solve using square roots:
  $$x^{2}+5=0$$
- step1: Add or subtract both sides:
  $$x^{2}=-5$$
- step2: Simplify the expression:
  $$x=\pm \sqrt{-5}$$
- step3: Simplify the expression:
  $$x=\pm \left(\sqrt{5}	imes iight)$$
- step4: Separate into possible cases:
  $$\begin{align}&x=\sqrt{5}	imes i\&x=-\sqrt{5}	imes i\end{align}$$
- step5: Rewrite:
  $$x_{1}=-\sqrt{5}	imes i,x_{2}=\sqrt{5}	imes i$$
Solve the equation $$ x^{2}-5=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
  $$x^{2}-5=0$$
- step1: Add or subtract both sides:
  $$x^{2}=5$$
- step2: Simplify the expression:
  $$x=\pm \sqrt{5}$$
- step3: Separate into possible cases:
  $$\begin{align}&x=\sqrt{5}\&x=-\sqrt{5}\end{align}$$
- step4: Rewrite:
  $$x_{1}=-\sqrt{5},x_{2}=\sqrt{5}$$
Solve the equation $$ x^{2}=-45 $$.
Solve the equation(The complex numbers system) by following steps:
- step0: Solve using square roots:
  $$x^{2}=-45$$
- step1: Simplify the expression:
  $$x=\pm \sqrt{-45}$$
- step2: Simplify the expression:
  $$x=\pm \left(3\sqrt{5}	imes iight)$$
- step3: Separate into possible cases:
  $$\begin{align}&x=3\sqrt{5}	imes i\&x=-3\sqrt{5}	imes i\end{align}$$
- step4: Rewrite:
  $$x_{1}=-3\sqrt{5}	imes i,x_{2}=3\sqrt{5}	imes i$$
Solve the equation $$ x^{2}=45 $$.
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
  $$x^{2}=45$$
- step1: Simplify the expression:
  $$x=\pm \sqrt{45}$$
- step2: Simplify the expression:
  $$x=\pm 3\sqrt{5}$$
- step3: Separate into possible cases:
  $$\begin{align}&x=3\sqrt{5}\&x=-3\sqrt{5}\end{align}$$
- step4: Rewrite:
  $$x_{1}=-3\sqrt{5},x_{2}=3\sqrt{5}$$
Let's match each equation with its corresponding solution(s):

1. **Equation:** $$ x^{2}=25 $$  
   **Solution:** $$ x = -5, 5 $$  
   **Match:** $$ 5 $$ and $$ -5 $$

2. **Equation:** $$ x^{2}=-25 $$  
   **Solution:** $$ x = -5i, 5i $$  
   **Match:** $$ \pm 5i $$

3. **Equation:** $$ x^{2}+5=0 $$  
   **Solution:** $$ x = -i\sqrt{5}, i\sqrt{5} $$  
   **Match:** $$ \pm i\sqrt{5} $$

4. **Equation:** $$ x^{2}-5=0 $$  
   **Solution:** $$ x = -\sqrt{5}, \sqrt{5} $$  
   **Match:** $$ \pm \sqrt{5} $$

5. **Equation:** $$ x^{2}=-45 $$  
   **Solution:** $$ x = -3i\sqrt{5}, 3i\sqrt{5} $$  
   **Match:** $$ \pm 3i\sqrt{5} $$

6. **Equation:** $$ x^{2}=45 $$  
   **Solution:** $$ x = -3\sqrt{5}, 3\sqrt{5} $$  
   **Match:** $$ \pm 3\sqrt{5} $$

7. **Equation:** $$ x-5=0 $$  
   **Solution:** $$ x = 5 $$  
   **Match:** $$ 5 $$

8. **Equation:** $$ x+5=0 $$  
   **Solution:** $$ x = -5 $$  
   **Match:** $$ -5 $$

### Summary of Matches:
- 1: $$ 5, -5 $$
- 2: $$ \pm 5i $$
- 3: $$ \pm i\sqrt{5} $$
- 4: $$ \pm \sqrt{5} $$
- 5: $$ \pm 3i\sqrt{5} $$
- 6: $$ \pm 3\sqrt{5} $$
- 7: $$ 5 $$
- 8: $$ -5 $$
1. $$ x^{2}=25 $$ → $$ 5, -5 $$ 2. $$ x^{2}=-25 $$ → $$ \pm 5i $$ 3. $$ x^{2}+5=0 $$ → $$ \pm i\sqrt{5} $$ 4. $$ x^{2}-5=0 $$ → $$ \pm \sqrt{5} $$ 5. $$ x^{2}=-45 $$ → $$ \pm 3i\sqrt{5} $$ 6. $$ x^{2}=45 $$ → $$ \pm 3\sqrt{5} $$ 7. $$ x-5=0 $$ → $$ 5 $$ 8. $$ x+5=0 $$ → $$ -5 $$

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