Question

Use the quadratic formula to solve x2 + 5x = –2

Answer 1

The general formula for a quadratic equation is:

Ax² + Bx + C = 0

The quadratic formula is expressed as:

x1 = -B + √(B²-4AC) / 2A
x2 = -B - √(B²-4AC) / 2A

The equation is:

x2 + 5x = –2
x2 + 5x + 2 = 0

x1 = -5 + √(5²-4(1)(2)) / 2(2) = -0.22 
x2 = -5 - √(5²-4(1)(2)) / 2(2) = -2.28

Answer 2

$x^2+5x=-2\\x^2+5x+2=0\\\\a=1;\ b=5;\ c=2\\\Delta=b^2-4ac\\\\\Delta=5^2-4\cdot1\cdot2=25-8=17 \ \textgreater \ 0\\\\then\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\x_1=\dfrac{-5-\sqrt{17}}{2\cdot1}=\boxed{\dfrac{-5-\sqrt{17}}{2}}\\\\x_2=\dfrac{-5+\sqrt{17}}{2\cdot1}=\boxed{\dfrac{-5+\sqrt{17}}{2}}$