Mathematics: Which equation has the same solutions as x^2+6x−7=0? Question options: (x+3)^2=2 (x−3)^2=2 (x+3)^2=16 (x−3)^2=16

Which equation has the same solutions as x^2+6x−7=0?

GaudySky

20.01.2022

${(x + 3)}^{2} = 16$

Step-by-step explanation:

The given equation is

${x}^{2} + 6x - 7 = 0$

To find the equation that has the same solution, we complete the square.

Add the square of half the coefficient of x to both sides

${x}^{2} + 6x + {3}^{2} = {3}^{2} + 7$

This becomes:

${x}^{2} + 6x + 9 = 9 + 7$

Factor the first three terms to get a perfect square;

${(x + 3)}^{2} = 16$

The correct answer is C

0,0(0 оценок)