Question

X^2+10x+7=0 using complete the square method

Answer 1

x₁ = -9.24265

x₂ = -0.75735

Explanation:

x² + 10x + 7 = 0

x = {-10±√((10²)-(4*1*7))} / (2*1)

x = {-10±√(100-28)} / 2

x = {-10±√72} / 2

x = {-10±8.4853} /2

x₁ = {-10-8.4853} / 2 = -18.4853/2 = -9.24265

x₂ = {-10+8.4853} / 2 = -1.5147/2 = -0.75735

Check:

x₁

-9.24265² + 10*-9.24265 + 7 = 0

85.4265 - 92.4265 + 7 = 0

x₂

-0.75735² + 10*-0.75735 + 7 = 0

0.5735 - 7.5735 + 7 = 0

Answer 2

`x=-5 \pm 3√(2)`

Explanation:

`x^2 +10x+7=0 \\ \\ x^2+10x=-7 \\ \\ x^2+10x+25=18 \\ \\ (x+5)^2=18 \\ \\ x+5=\pm 3√(2) \\ \\ x=-5 \pm 3√(2)`