4x^2+5x=120

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Solution for 4x^2+5x=120 equation:


Simplifying
4x2 + 5x = 120

Reorder the terms:
5x + 4x2 = 120

Solving
5x + 4x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 5x + 4x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 5x + 4x2 = 0

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

Divide each side by '4'.
-30 + 1.25x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 1.25x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 1.25x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 1.25x + x2 = 0 + 30
1.25x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
1.25x + x2 = 30

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 30 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 30 + 0.390625

Combine like terms: 30 + 0.390625 = 30.390625
0.390625 + 1.25x + x2 = 30.390625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 30.390625

Calculate the square root of the right side: 5.512769268

Break this problem into two subproblems by setting 
(x + 0.625) equal to 5.512769268 and -5.512769268.

Subproblem 1

x + 0.625 = 5.512769268 Simplifying x + 0.625 = 5.512769268 Reorder the terms: 0.625 + x = 5.512769268 Solving 0.625 + x = 5.512769268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 5.512769268 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 5.512769268 + -0.625 x = 5.512769268 + -0.625 Combine like terms: 5.512769268 + -0.625 = 4.887769268 x = 4.887769268 Simplifying x = 4.887769268

Subproblem 2

x + 0.625 = -5.512769268 Simplifying x + 0.625 = -5.512769268 Reorder the terms: 0.625 + x = -5.512769268 Solving 0.625 + x = -5.512769268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -5.512769268 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -5.512769268 + -0.625 x = -5.512769268 + -0.625 Combine like terms: -5.512769268 + -0.625 = -6.137769268 x = -6.137769268 Simplifying x = -6.137769268

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.887769268, -6.137769268}

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