8x^2+12x-14=0

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Solution for 8x^2+12x-14=0 equation:


Simplifying
8x2 + 12x + -14 = 0

Reorder the terms:
-14 + 12x + 8x2 = 0

Solving
-14 + 12x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 6x + 4x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-7 + 6x + 4x2)' equal to zero and attempt to solve: Simplifying -7 + 6x + 4x2 = 0 Solving -7 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 1.5x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 1.5x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 1.5x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 1.5x + x2 = 0 + 1.75 1.5x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 1.5x + x2 = 1.75 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 = 1.75 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1.75 + 0.5625 Combine like terms: 1.75 + 0.5625 = 2.3125 0.5625 + 1.5x + x2 = 2.3125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (x + 0.75) equal to 1.520690633 and -1.520690633.

Subproblem 1

x + 0.75 = 1.520690633 Simplifying x + 0.75 = 1.520690633 Reorder the terms: 0.75 + x = 1.520690633 Solving 0.75 + x = 1.520690633 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 = 1.520690633 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.520690633 + -0.75 x = 1.520690633 + -0.75 Combine like terms: 1.520690633 + -0.75 = 0.770690633 x = 0.770690633 Simplifying x = 0.770690633

Subproblem 2

x + 0.75 = -1.520690633 Simplifying x + 0.75 = -1.520690633 Reorder the terms: 0.75 + x = -1.520690633 Solving 0.75 + x = -1.520690633 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 = -1.520690633 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.520690633 + -0.75 x = -1.520690633 + -0.75 Combine like terms: -1.520690633 + -0.75 = -2.270690633 x = -2.270690633 Simplifying x = -2.270690633

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.770690633, -2.270690633}

Solution

x = {0.770690633, -2.270690633}

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