4x^2+15x-60=0

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Solution for 4x^2+15x-60=0 equation:


Simplifying
4x2 + 15x + -60 = 0

Reorder the terms:
-60 + 15x + 4x2 = 0

Solving
-60 + 15x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-15 + 3.75x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 3.75x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 3.75x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 3.75x + x2 = 0 + 15
3.75x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
3.75x + x2 = 15

The x term is 3.75x.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75x + 3.515625 + x2 = 15 + 3.515625

Reorder the terms:
3.515625 + 3.75x + x2 = 15 + 3.515625

Combine like terms: 15 + 3.515625 = 18.515625
3.515625 + 3.75x + x2 = 18.515625

Factor a perfect square on the left side:
(x + 1.875)(x + 1.875) = 18.515625

Calculate the square root of the right side: 4.30297862

Break this problem into two subproblems by setting 
(x + 1.875) equal to 4.30297862 and -4.30297862.

Subproblem 1

x + 1.875 = 4.30297862 Simplifying x + 1.875 = 4.30297862 Reorder the terms: 1.875 + x = 4.30297862 Solving 1.875 + x = 4.30297862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 4.30297862 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 4.30297862 + -1.875 x = 4.30297862 + -1.875 Combine like terms: 4.30297862 + -1.875 = 2.42797862 x = 2.42797862 Simplifying x = 2.42797862

Subproblem 2

x + 1.875 = -4.30297862 Simplifying x + 1.875 = -4.30297862 Reorder the terms: 1.875 + x = -4.30297862 Solving 1.875 + x = -4.30297862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -4.30297862 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -4.30297862 + -1.875 x = -4.30297862 + -1.875 Combine like terms: -4.30297862 + -1.875 = -6.17797862 x = -6.17797862 Simplifying x = -6.17797862

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.42797862, -6.17797862}

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