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.)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Algebra Questions

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.)