4x^2-3x=95

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Solution for 4x^2-3x=95 equation:


Simplifying
4x2 + -3x = 95

Reorder the terms:
-3x + 4x2 = 95

Solving
-3x + 4x2 = 95

Solving for variable 'x'.

Reorder the terms:
-95 + -3x + 4x2 = 95 + -95

Combine like terms: 95 + -95 = 0
-95 + -3x + 4x2 = 0

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

Divide each side by '4'.
-23.75 + -0.75x + x2 = 0

Move the constant term to the right:

Add '23.75' to each side of the equation.
-23.75 + -0.75x + 23.75 + x2 = 0 + 23.75

Reorder the terms:
-23.75 + 23.75 + -0.75x + x2 = 0 + 23.75

Combine like terms: -23.75 + 23.75 = 0.00
0.00 + -0.75x + x2 = 0 + 23.75
-0.75x + x2 = 0 + 23.75

Combine like terms: 0 + 23.75 = 23.75
-0.75x + x2 = 23.75

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 23.75 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 23.75 + 0.140625

Combine like terms: 23.75 + 0.140625 = 23.890625
0.140625 + -0.75x + x2 = 23.890625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 23.890625

Calculate the square root of the right side: 4.887803699

Break this problem into two subproblems by setting 
(x + -0.375) equal to 4.887803699 and -4.887803699.

Subproblem 1

x + -0.375 = 4.887803699 Simplifying x + -0.375 = 4.887803699 Reorder the terms: -0.375 + x = 4.887803699 Solving -0.375 + x = 4.887803699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 4.887803699 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 4.887803699 + 0.375 x = 4.887803699 + 0.375 Combine like terms: 4.887803699 + 0.375 = 5.262803699 x = 5.262803699 Simplifying x = 5.262803699

Subproblem 2

x + -0.375 = -4.887803699 Simplifying x + -0.375 = -4.887803699 Reorder the terms: -0.375 + x = -4.887803699 Solving -0.375 + x = -4.887803699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -4.887803699 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -4.887803699 + 0.375 x = -4.887803699 + 0.375 Combine like terms: -4.887803699 + 0.375 = -4.512803699 x = -4.512803699 Simplifying x = -4.512803699

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.262803699, -4.512803699}

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