4x^2+87x+124=0

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Solution for 4x^2+87x+124=0 equation:


Simplifying
4x2 + 87x + 124 = 0

Reorder the terms:
124 + 87x + 4x2 = 0

Solving
124 + 87x + 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'.
31 + 21.75x + x2 = 0

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + 21.75x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + 21.75x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 21.75x + x2 = 0 + -31
21.75x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
21.75x + x2 = -31

The x term is 21.75x.  Take half its coefficient (10.875).
Square it (118.265625) and add it to both sides.

Add '118.265625' to each side of the equation.
21.75x + 118.265625 + x2 = -31 + 118.265625

Reorder the terms:
118.265625 + 21.75x + x2 = -31 + 118.265625

Combine like terms: -31 + 118.265625 = 87.265625
118.265625 + 21.75x + x2 = 87.265625

Factor a perfect square on the left side:
(x + 10.875)(x + 10.875) = 87.265625

Calculate the square root of the right side: 9.341607196

Break this problem into two subproblems by setting 
(x + 10.875) equal to 9.341607196 and -9.341607196.

Subproblem 1

x + 10.875 = 9.341607196 Simplifying x + 10.875 = 9.341607196 Reorder the terms: 10.875 + x = 9.341607196 Solving 10.875 + x = 9.341607196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.875' to each side of the equation. 10.875 + -10.875 + x = 9.341607196 + -10.875 Combine like terms: 10.875 + -10.875 = 0.000 0.000 + x = 9.341607196 + -10.875 x = 9.341607196 + -10.875 Combine like terms: 9.341607196 + -10.875 = -1.533392804 x = -1.533392804 Simplifying x = -1.533392804

Subproblem 2

x + 10.875 = -9.341607196 Simplifying x + 10.875 = -9.341607196 Reorder the terms: 10.875 + x = -9.341607196 Solving 10.875 + x = -9.341607196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.875' to each side of the equation. 10.875 + -10.875 + x = -9.341607196 + -10.875 Combine like terms: 10.875 + -10.875 = 0.000 0.000 + x = -9.341607196 + -10.875 x = -9.341607196 + -10.875 Combine like terms: -9.341607196 + -10.875 = -20.216607196 x = -20.216607196 Simplifying x = -20.216607196

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.533392804, -20.216607196}

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