Solve. First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. (Enter your
answers as a comma-separated list.)

Ask by Ortega Johnston. in the United States

Nov 20,2024

Question

Solve. First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. (Enter your
answers as a comma-separated list.)

Ask by Ortega Johnston. in the United States

Nov 20,2024

UpStudy AI · Accepted Answer

Solve the equation $$ 4x^2-6x=3 $$.
Solve the quadratic equation by following steps:
- step0: Solve using the quadratic formula:
  $$4x^{2}-6x=3$$
- step1: Move the expression to the left side:
  $$4x^{2}-6x-3=0$$
- step2: Solve using the quadratic formula:
  $$x=\frac{6\pm \sqrt{\left(-6ight)^{2}-4	imes 4\left(-3ight)}}{2	imes 4}$$
- step3: Simplify the expression:
  $$x=\frac{6\pm \sqrt{\left(-6ight)^{2}-4	imes 4\left(-3ight)}}{8}$$
- step4: Simplify the expression:
  $$x=\frac{6\pm \sqrt{84}}{8}$$
- step5: Simplify the expression:
  $$x=\frac{6\pm 2\sqrt{21}}{8}$$
- step6: Separate into possible cases:
  $$\begin{align}&x=\frac{6+2\sqrt{21}}{8}\&x=\frac{6-2\sqrt{21}}{8}\end{align}$$
- step7: Simplify the expression:
  $$\begin{align}&x=\frac{3+\sqrt{21}}{4}\&x=\frac{6-2\sqrt{21}}{8}\end{align}$$
- step8: Simplify the expression:
  $$\begin{align}&x=\frac{3+\sqrt{21}}{4}\&x=\frac{3-\sqrt{21}}{4}\end{align}$$
- step9: Rewrite:
  $$x_{1}=\frac{3-\sqrt{21}}{4},x_{2}=\frac{3+\sqrt{21}}{4}$$
The solutions to the equation $$4x^{2}-6x=3$$ are $$x=\frac{3-\sqrt{21}}{4}$$ and $$x=\frac{3+\sqrt{21}}{4}$$.
$$ x=\frac{3-\sqrt{21}}{4}, x=\frac{3+\sqrt{21}}{4} $$

Solve. First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. (Enter your
answers as a comma-separated list.)

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Solve. First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. (Enter your answers as a comma-separated list.)

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Solve. First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. (Enter your
answers as a comma-separated list.)