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Simplifying 0 = -16x2 + 12x + 14 Reorder the terms: 0 = 14 + 12x + -16x2 Solving 0 = 14 + 12x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -14 = -14 -14 + -12x + 16x2 = 14 + 12x + -16x2 + -14 + -12x + 16x2 Reorder the terms: -14 + -12x + 16x2 = 14 + -14 + 12x + -12x + -16x2 + 16x2 Combine like terms: 14 + -14 = 0 -14 + -12x + 16x2 = 0 + 12x + -12x + -16x2 + 16x2 -14 + -12x + 16x2 = 12x + -12x + -16x2 + 16x2 Combine like terms: 12x + -12x = 0 -14 + -12x + 16x2 = 0 + -16x2 + 16x2 -14 + -12x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -14 + -12x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -6x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -6x + 8x2)' equal to zero and attempt to solve: Simplifying -7 + -6x + 8x2 = 0 Solving -7 + -6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -0.75x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.75x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.75x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.75x + x2 = 0 + 0.875 -0.75x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.75x + x2 = 0.875 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 0.875 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.875 + 0.140625 Combine like terms: 0.875 + 0.140625 = 1.015625 0.140625 + -0.75x + x2 = 1.015625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (x + -0.375) equal to 1.007782219 and -1.007782219.Subproblem 1
x + -0.375 = 1.007782219 Simplifying x + -0.375 = 1.007782219 Reorder the terms: -0.375 + x = 1.007782219 Solving -0.375 + x = 1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.007782219 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.007782219 + 0.375 x = 1.007782219 + 0.375 Combine like terms: 1.007782219 + 0.375 = 1.382782219 x = 1.382782219 Simplifying x = 1.382782219Subproblem 2
x + -0.375 = -1.007782219 Simplifying x + -0.375 = -1.007782219 Reorder the terms: -0.375 + x = -1.007782219 Solving -0.375 + x = -1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.007782219 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.007782219 + 0.375 x = -1.007782219 + 0.375 Combine like terms: -1.007782219 + 0.375 = -0.632782219 x = -0.632782219 Simplifying x = -0.632782219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.382782219, -0.632782219}Solution
x = {1.382782219, -0.632782219}
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