4x^2-5x-12=3

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Solution for 4x^2-5x-12=3 equation:


Simplifying
4x2 + -5x + -12 = 3

Reorder the terms:
-12 + -5x + 4x2 = 3

Solving
-12 + -5x + 4x2 = 3

Solving for variable 'x'.

Reorder the terms:
-12 + -3 + -5x + 4x2 = 3 + -3

Combine like terms: -12 + -3 = -15
-15 + -5x + 4x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-15 + -5x + 4x2 = 0

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

Divide each side by '4'.
-3.75 + -1.25x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -1.25x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -1.25x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -1.25x + x2 = 0 + 3.75
-1.25x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-1.25x + x2 = 3.75

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 = 3.75 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 3.75 + 0.390625

Combine like terms: 3.75 + 0.390625 = 4.140625
0.390625 + -1.25x + x2 = 4.140625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + -0.625) equal to 2.034852575 and -2.034852575.

Subproblem 1

x + -0.625 = 2.034852575 Simplifying x + -0.625 = 2.034852575 Reorder the terms: -0.625 + x = 2.034852575 Solving -0.625 + x = 2.034852575 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 = 2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.034852575 + 0.625 x = 2.034852575 + 0.625 Combine like terms: 2.034852575 + 0.625 = 2.659852575 x = 2.659852575 Simplifying x = 2.659852575

Subproblem 2

x + -0.625 = -2.034852575 Simplifying x + -0.625 = -2.034852575 Reorder the terms: -0.625 + x = -2.034852575 Solving -0.625 + x = -2.034852575 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 = -2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.034852575 + 0.625 x = -2.034852575 + 0.625 Combine like terms: -2.034852575 + 0.625 = -1.409852575 x = -1.409852575 Simplifying x = -1.409852575

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.659852575, -1.409852575}

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