Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. X^2 + 5x-10=0

Answer 1

$(*)\\(a+b)^2=a^2+2ab+b^2$

$x^2+5x-10=0\ \ \ |+10\\\\x^2+2\cdot x\cdot2.5=10\ \ \ |+2.5^2\\\\\underbrace{x^2+2\cdot x\cdot2.5+2.5^2}_{(*)}=10+2.5^2\\\\(x+2.5)^2=16.25\to x+2.5=\pm\sqrt{16.25}\\\\x+2.5\approx-4.03\ \vee\ x+2.5=4.03\ \ \ |-2.5\\\\x\approx-6.53\ \vee\ x\approx1.53$