Use factorization or complete the quadratic forms to solve the problem
If you use the factorization,
x² + 3x = 40
move all terms to the left side, so the right side is equal to 0
x² + 3x - 40 = 0
two factors of -40 is 8 and -5
x² + 8x - 5x - 40 = 0
(x² + 8x) - (5x + 40) = 0
x(x + 8) - 5 (x + 8) = 0
(x - 5)(x + 8) = 0
x = 5 or x = -8
If you use completing quadratic forms
x² + 3x = 40
I multiply the two sides by 4 to make a complete quadratic forms
4x² + 12x = 160
add both side with 9
4x² + 12x + 9 = 160 + 9
(2x + 3)² = 169
(2x + 3) = + √169 or (2x + 3) = -√169
∴ 2x + 3 = 13
2x = 10
x = 5
∴ 2x + 3 = -13
2x = -16
x = -8
THE SOLUTION
x = 5
x = -8