4x^2+42x-59=0

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Solution for 4x^2+42x-59=0 equation:


Simplifying
4x2 + 42x + -59 = 0

Reorder the terms:
-59 + 42x + 4x2 = 0

Solving
-59 + 42x + 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'.
-14.75 + 10.5x + x2 = 0

Move the constant term to the right:

Add '14.75' to each side of the equation.
-14.75 + 10.5x + 14.75 + x2 = 0 + 14.75

Reorder the terms:
-14.75 + 14.75 + 10.5x + x2 = 0 + 14.75

Combine like terms: -14.75 + 14.75 = 0.00
0.00 + 10.5x + x2 = 0 + 14.75
10.5x + x2 = 0 + 14.75

Combine like terms: 0 + 14.75 = 14.75
10.5x + x2 = 14.75

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = 14.75 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = 14.75 + 27.5625

Combine like terms: 14.75 + 27.5625 = 42.3125
27.5625 + 10.5x + x2 = 42.3125

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 42.3125

Calculate the square root of the right side: 6.504805916

Break this problem into two subproblems by setting 
(x + 5.25) equal to 6.504805916 and -6.504805916.

Subproblem 1

x + 5.25 = 6.504805916 Simplifying x + 5.25 = 6.504805916 Reorder the terms: 5.25 + x = 6.504805916 Solving 5.25 + x = 6.504805916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 6.504805916 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 6.504805916 + -5.25 x = 6.504805916 + -5.25 Combine like terms: 6.504805916 + -5.25 = 1.254805916 x = 1.254805916 Simplifying x = 1.254805916

Subproblem 2

x + 5.25 = -6.504805916 Simplifying x + 5.25 = -6.504805916 Reorder the terms: 5.25 + x = -6.504805916 Solving 5.25 + x = -6.504805916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -6.504805916 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -6.504805916 + -5.25 x = -6.504805916 + -5.25 Combine like terms: -6.504805916 + -5.25 = -11.754805916 x = -11.754805916 Simplifying x = -11.754805916

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.254805916, -11.754805916}

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