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Simplifying 8x2 = 12x + 14 Reorder the terms: 8x2 = 14 + 12x Solving 8x2 = 14 + 12x Solving for variable 'x'. Reorder the terms: -14 + -12x + 8x2 = 14 + 12x + -14 + -12x Reorder the terms: -14 + -12x + 8x2 = 14 + -14 + 12x + -12x Combine like terms: 14 + -14 = 0 -14 + -12x + 8x2 = 0 + 12x + -12x -14 + -12x + 8x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -14 + -12x + 8x2 = 0 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 = 2.270690633 x = 2.270690633 Simplifying x = 2.270690633Subproblem 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 = -0.770690633 x = -0.770690633 Simplifying x = -0.770690633Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.270690633, -0.770690633}Solution
x = {2.270690633, -0.770690633}
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