Solve the quadratic equation by completing the square.

The solution set is .
(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

Ask by Haynes Ross. in the United States

Mar 06,2025

Question

Solve the quadratic equation by completing the square. $$ x^{2}-10 x-6=0 $$ The solution set is $$ \} $$. (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

UpStudy AI · Accepted Answer

Solve the equation $$ x^{2}-10x-6=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve using the quadratic formula:
  $$x^{2}-10x-6=0$$
- step1: Solve using the quadratic formula:
  $$x=\frac{10\pm \sqrt{\left(-10ight)^{2}-4\left(-6ight)}}{2}$$
- step2: Simplify the expression:
  $$x=\frac{10\pm \sqrt{124}}{2}$$
- step3: Simplify the expression:
  $$x=\frac{10\pm 2\sqrt{31}}{2}$$
- step4: Separate into possible cases:
  $$\begin{align}&x=\frac{10+2\sqrt{31}}{2}\&x=\frac{10-2\sqrt{31}}{2}\end{align}$$
- step5: Simplify the expression:
  $$\begin{align}&x=5+\sqrt{31}\&x=\frac{10-2\sqrt{31}}{2}\end{align}$$
- step6: Simplify the expression:
  $$\begin{align}&x=5+\sqrt{31}\&x=5-\sqrt{31}\end{align}$$
- step7: Rewrite:
  $$x_{1}=5-\sqrt{31},x_{2}=5+\sqrt{31}$$
The solutions to the quadratic equation $$x^{2}-10x-6=0$$ by completing the square are $$x_{1}=5-\sqrt{31}$$ and $$x_{2}=5+\sqrt{31}$$.
The solutions are $$ x = 5 - \sqrt{31} $$ and $$ x = 5 + \sqrt{31} $$.

Solve the quadratic equation by completing the square.

The solution set is .
(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

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Solve the quadratic equation by completing the square. The solution set is . (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)