6x^2+9x-12=143

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Solution for 6x^2+9x-12=143 equation:


Simplifying
6x2 + 9x + -12 = 143

Reorder the terms:
-12 + 9x + 6x2 = 143

Solving
-12 + 9x + 6x2 = 143

Solving for variable 'x'.

Reorder the terms:
-12 + -143 + 9x + 6x2 = 143 + -143

Combine like terms: -12 + -143 = -155
-155 + 9x + 6x2 = 143 + -143

Combine like terms: 143 + -143 = 0
-155 + 9x + 6x2 = 0

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

Divide each side by '6'.
-25.83333333 + 1.5x + x2 = 0

Move the constant term to the right:

Add '25.83333333' to each side of the equation.
-25.83333333 + 1.5x + 25.83333333 + x2 = 0 + 25.83333333

Reorder the terms:
-25.83333333 + 25.83333333 + 1.5x + x2 = 0 + 25.83333333

Combine like terms: -25.83333333 + 25.83333333 = 0.00000000
0.00000000 + 1.5x + x2 = 0 + 25.83333333
1.5x + x2 = 0 + 25.83333333

Combine like terms: 0 + 25.83333333 = 25.83333333
1.5x + x2 = 25.83333333

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 25.83333333 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 25.83333333 + 0.5625

Combine like terms: 25.83333333 + 0.5625 = 26.39583333
0.5625 + 1.5x + x2 = 26.39583333

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 26.39583333

Calculate the square root of the right side: 5.137687547

Break this problem into two subproblems by setting 
(x + 0.75) equal to 5.137687547 and -5.137687547.

Subproblem 1

x + 0.75 = 5.137687547 Simplifying x + 0.75 = 5.137687547 Reorder the terms: 0.75 + x = 5.137687547 Solving 0.75 + x = 5.137687547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 5.137687547 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 5.137687547 + -0.75 x = 5.137687547 + -0.75 Combine like terms: 5.137687547 + -0.75 = 4.387687547 x = 4.387687547 Simplifying x = 4.387687547

Subproblem 2

x + 0.75 = -5.137687547 Simplifying x + 0.75 = -5.137687547 Reorder the terms: 0.75 + x = -5.137687547 Solving 0.75 + x = -5.137687547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -5.137687547 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -5.137687547 + -0.75 x = -5.137687547 + -0.75 Combine like terms: -5.137687547 + -0.75 = -5.887687547 x = -5.887687547 Simplifying x = -5.887687547

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.387687547, -5.887687547}

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