What are the solutions of x 2 6x 6 10

Asked by admin @ 02/08/2021 in Math viewed by 433 People

What are the solutions of x^2+6x-6=10

Answered by admin @ 02/08/2021

Answer:

$\Large\boxed{\mathsf{X=2, X=-8}}$

Step-by-step explanation:

GIVEN:

x²+6x-6=10

TO FIND:

The solutions of x²+6x-6=10.

TO SOLVE:

With quadratic equation.

SOLUTIONS:

First, thing you do is subtract by 10 from both sides.

$\displaystyle \mathsf{x^2+6x-6-10=10-10}}}$

Solve.

$\displaystyle \mathsf{x^2+6x-16=0}$

$\Large\boxed{\mathsf{QUADRATIC \quad EQUATION}}$

$\displaystyle \mathsf{AX^2+BX+C=0}$

$\displaystyle \mathsf{\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$

$\displaystyle \mathsf{A=1}\\\\\displaystyle \mathsf{B=6}\\\\\displaystyle \mathsf{C=(-16)}\\\\$

$\displaystyle \mathsf{\frac{-6\pm \sqrt{6^2-4*\:1\left(-16\right)}}{2* \:1}}}}$

$\displaystyle\mathsf{6^2+4*1*16=\sqrt{100}}}$

$\displaystyle \mathsf{\frac{-6+\sqrt{100}}{2*\:1}}}$

Multiply.

2*1=2

$\displaystyle \mathsf{\frac{-6+\sqrt{100}}{2}}}$

$\displaystyle \mathsf{\sqrt{100}=10^2=10\times10=100=10}}}}$

$\displaystyle \mathsf{\frac{-6+10}{2}}$

Add and subtract.

$\displaystyle \mathsf{-6+10=4}$

Divide.

$\displaystyle \mathsf{4\div2=2}$

$\Large\boxed{\longrightarrow \mathsf{X=2}}$

$\displaystyle \mathsf{\frac{-6-\sqrt{6^2-4\cdot \:1\left(-16\right)}}{2\cdot \:1}}}=\boxed{-8}$

$\Large\boxed{\mathsf{\longrightarrow X=-8}}$

In conclusion, the solutions of x²+6x-6=10 is x=2, and x=-8, which is our final answer.

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