4x^2-112x-375=0

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Solution for 4x^2-112x-375=0 equation:


Simplifying
4x2 + -112x + -375 = 0

Reorder the terms:
-375 + -112x + 4x2 = 0

Solving
-375 + -112x + 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'.
-93.75 + -28x + x2 = 0

Move the constant term to the right:

Add '93.75' to each side of the equation.
-93.75 + -28x + 93.75 + x2 = 0 + 93.75

Reorder the terms:
-93.75 + 93.75 + -28x + x2 = 0 + 93.75

Combine like terms: -93.75 + 93.75 = 0.00
0.00 + -28x + x2 = 0 + 93.75
-28x + x2 = 0 + 93.75

Combine like terms: 0 + 93.75 = 93.75
-28x + x2 = 93.75

The x term is -28x.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28x + 196 + x2 = 93.75 + 196

Reorder the terms:
196 + -28x + x2 = 93.75 + 196

Combine like terms: 93.75 + 196 = 289.75
196 + -28x + x2 = 289.75

Factor a perfect square on the left side:
(x + -14)(x + -14) = 289.75

Calculate the square root of the right side: 17.022044531

Break this problem into two subproblems by setting 
(x + -14) equal to 17.022044531 and -17.022044531.

Subproblem 1

x + -14 = 17.022044531 Simplifying x + -14 = 17.022044531 Reorder the terms: -14 + x = 17.022044531 Solving -14 + x = 17.022044531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 17.022044531 + 14 Combine like terms: -14 + 14 = 0 0 + x = 17.022044531 + 14 x = 17.022044531 + 14 Combine like terms: 17.022044531 + 14 = 31.022044531 x = 31.022044531 Simplifying x = 31.022044531

Subproblem 2

x + -14 = -17.022044531 Simplifying x + -14 = -17.022044531 Reorder the terms: -14 + x = -17.022044531 Solving -14 + x = -17.022044531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -17.022044531 + 14 Combine like terms: -14 + 14 = 0 0 + x = -17.022044531 + 14 x = -17.022044531 + 14 Combine like terms: -17.022044531 + 14 = -3.022044531 x = -3.022044531 Simplifying x = -3.022044531

Solution

The solution to the problem is based on the solutions from the subproblems. x = {31.022044531, -3.022044531}

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