Solve the quadratic equation by completing the square.

First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
Form:
Solution:

Ask by Guerrero Kelley. in the United States

Jan 24,2025

Question

Solve the quadratic equation by completing the square.

First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
Form:
Solution:

Ask by Guerrero Kelley. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

Solve the equation $$ x^{2}-14x+35=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve using the quadratic formula:
  $$x^{2}-14x+35=0$$
- step1: Solve using the quadratic formula:
  $$x=\frac{14\pm \sqrt{\left(-14ight)^{2}-4	imes 35}}{2}$$
- step2: Simplify the expression:
  $$x=\frac{14\pm \sqrt{56}}{2}$$
- step3: Simplify the expression:
  $$x=\frac{14\pm 2\sqrt{14}}{2}$$
- step4: Separate into possible cases:
  $$\begin{align}&x=\frac{14+2\sqrt{14}}{2}\&x=\frac{14-2\sqrt{14}}{2}\end{align}$$
- step5: Simplify the expression:
  $$\begin{align}&x=7+\sqrt{14}\&x=\frac{14-2\sqrt{14}}{2}\end{align}$$
- step6: Simplify the expression:
  $$\begin{align}&x=7+\sqrt{14}\&x=7-\sqrt{14}\end{align}$$
- step7: Rewrite:
  $$x_{1}=7-\sqrt{14},x_{2}=7+\sqrt{14}$$
The solutions to the quadratic equation $$x^{2}-14x+35=0$$ by completing the square are $$x_{1}=7-\sqrt{14}$$ and $$x_{2}=7+\sqrt{14}$$.
$$ x = 7 - \sqrt{14}, $$ $$ x = 7 + \sqrt{14} $$

Solve the quadratic equation by completing the square.

First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
Form:
Solution:

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Solve the quadratic equation by completing the square. First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. Form: Solution:

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Latest Algebra Questions

Solve the quadratic equation by completing the square.

First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
Form:
Solution: