(4x-3)x=114

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Solution for (4x-3)x=114 equation:


Simplifying
(4x + -3) * x = 114

Reorder the terms:
(-3 + 4x) * x = 114

Reorder the terms for easier multiplication:
x(-3 + 4x) = 114
(-3 * x + 4x * x) = 114
(-3x + 4x2) = 114

Solving
-3x + 4x2 = 114

Solving for variable 'x'.

Reorder the terms:
-114 + -3x + 4x2 = 114 + -114

Combine like terms: 114 + -114 = 0
-114 + -3x + 4x2 = 0

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

Divide each side by '4'.
-28.5 + -0.75x + x2 = 0

Move the constant term to the right:

Add '28.5' to each side of the equation.
-28.5 + -0.75x + 28.5 + x2 = 0 + 28.5

Reorder the terms:
-28.5 + 28.5 + -0.75x + x2 = 0 + 28.5

Combine like terms: -28.5 + 28.5 = 0.0
0.0 + -0.75x + x2 = 0 + 28.5
-0.75x + x2 = 0 + 28.5

Combine like terms: 0 + 28.5 = 28.5
-0.75x + x2 = 28.5

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 = 28.5 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 28.5 + 0.140625

Combine like terms: 28.5 + 0.140625 = 28.640625
0.140625 + -0.75x + x2 = 28.640625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 28.640625

Calculate the square root of the right side: 5.351693657

Break this problem into two subproblems by setting 
(x + -0.375) equal to 5.351693657 and -5.351693657.

Subproblem 1

x + -0.375 = 5.351693657 Simplifying x + -0.375 = 5.351693657 Reorder the terms: -0.375 + x = 5.351693657 Solving -0.375 + x = 5.351693657 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 = 5.351693657 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 5.351693657 + 0.375 x = 5.351693657 + 0.375 Combine like terms: 5.351693657 + 0.375 = 5.726693657 x = 5.726693657 Simplifying x = 5.726693657

Subproblem 2

x + -0.375 = -5.351693657 Simplifying x + -0.375 = -5.351693657 Reorder the terms: -0.375 + x = -5.351693657 Solving -0.375 + x = -5.351693657 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 = -5.351693657 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -5.351693657 + 0.375 x = -5.351693657 + 0.375 Combine like terms: -5.351693657 + 0.375 = -4.976693657 x = -4.976693657 Simplifying x = -4.976693657

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.726693657, -4.976693657}

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