Question

Solve the following equation. Give each answer correct to two decimal places. X^2 − 4x − 7 = 0

Answer 1

`x_1=2+√(11)\approx5.32\\x_2=2-√(11)\approx-1.32`

Explanation:

`x^2-4x-7=0\\x^2-4x-7+11=0+11\\x^2-4x+4=11\\(x-2)^2=11\\x-2=\pm√(11)\\x=2\pm√(11)\\\\x_1=2+√(11)\approx5.32\\x_2=2-√(11)\approx-1.32`

Answer 2

`x^2-4x-7=0\\D=b^2-4ac=(-4)^2-4*(-7)=16+28=44=√(44)^2=(2√(11))^2 \\ \\x_(1,2)=(4\pm2√(11) )/(2) =\bigg[^\bigg{2+√(11) \approx5,32}_\bigg{2-√(11) \approx-1,32}`

Ans: x₁≈5,32; x₂≈-1,32