Step 1: Divide equation by a number in front of the squared term. In this case we will divide by $ 2 $.
$$ \begin{aligned} 2x^2+8x-10 &= 0 \,\,\, ( \color{orangered}{ : 2 } ) \\[0.9 em ] x^2+4x-5 &=0 \end{aligned} $$Step 2: Keep all terms containing $ x $ on one side. Move $ -5 $ to the right.
$$ x^2+4x = 5 $$Step 3: Take half of the x -term coefficient and square it. Add this value to both sides.
The x-term coefficient = $ 4 $
The half of the x-term coefficient = $ 2 $
After squaring we have $ 2^2 = 4 $
When we add $ 4 $ to both sides we have:
$$ x^2+4x+4 = 5 + 4 $$Step 4: Simplify right side.
$$ x^2+4x+4 = 9 $$Step 5: Write the perfect square on the left.
$$ \left(x + 2 \right)^2 = 9 $$Step 6: Take the square root of both sides.
$$ x + 2 = \pm \sqrt { 9 } $$Step 7: Solve for $ x $.
$ x_1,x_2 = - 2 \pm \sqrt{ 9 } $
that is,
$ x_1 = -5 $
$ x_2 = 1 $