Solve the equation for all values of x by completing the square. x^2 - 11 = -4x

Question

asked Nov 4, 2023 120k views

1 Answer

LinX · Answer 1 · 2023-11-09T08:31:26+0000

Answer:

$x=-2-√(15)\\\\x=-2+√(15)$

Explanation:

Given equation:

x^2-11=-4x

Collect the terms in x on the left side and the constant on the right side of the equation:

$\implies x^2-11+4x=-4x+4x$

$\implies x^2+4x-11=0$

$\implies x^2+4x-11+11=0+11$

$\implies x^2+4x=11$

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

$\implies x^2+4x+\left((4)/(2)\right)^2=11+\left((4)/(2)\right)^2$

$\implies x^2+4x+4=11+4$

$\implies x^2+4x+4=15$

Factor the perfect trinomial on the left side of the equation:

$\implies (x+2)^2=15$

Square root both sides:

$\implies √((x+2)^2)=√(15)$

$\implies x+2=\pm√(15)$

Subtract 2 from both sides:

$\implies x+2-2=\pm√(15)-2$

$\implies x=-2\pm√(15)$

Therefore, the solutions are:

$x=-2-√(15), \;\; x=-2+√(15)$