2x^2+3-12=8x

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Solution for 2x^2+3-12=8x equation:


Simplifying
2x2 + 3 + -12 = 8x

Reorder the terms:
3 + -12 + 2x2 = 8x

Combine like terms: 3 + -12 = -9
-9 + 2x2 = 8x

Solving
-9 + 2x2 = 8x

Solving for variable 'x'.

Reorder the terms:
-9 + -8x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-9 + -8x + 2x2 = 0

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

Divide each side by '2'.
-4.5 + -4x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -4x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -4x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -4x + x2 = 0 + 4.5
-4x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-4x + x2 = 4.5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 4.5 + 4

Reorder the terms:
4 + -4x + x2 = 4.5 + 4

Combine like terms: 4.5 + 4 = 8.5
4 + -4x + x2 = 8.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + -2) equal to 2.915475947 and -2.915475947.

Subproblem 1

x + -2 = 2.915475947 Simplifying x + -2 = 2.915475947 Reorder the terms: -2 + x = 2.915475947 Solving -2 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.915475947 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.915475947 + 2 x = 2.915475947 + 2 Combine like terms: 2.915475947 + 2 = 4.915475947 x = 4.915475947 Simplifying x = 4.915475947

Subproblem 2

x + -2 = -2.915475947 Simplifying x + -2 = -2.915475947 Reorder the terms: -2 + x = -2.915475947 Solving -2 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.915475947 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.915475947 + 2 x = -2.915475947 + 2 Combine like terms: -2.915475947 + 2 = -0.915475947 x = -0.915475947 Simplifying x = -0.915475947

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.915475947, -0.915475947}

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