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Simplifying 0 = -16x2 + 14x + 6 Reorder the terms: 0 = 6 + 14x + -16x2 Solving 0 = 6 + 14x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -14x + 16x2 = 6 + 14x + -16x2 + -6 + -14x + 16x2 Reorder the terms: -6 + -14x + 16x2 = 6 + -6 + 14x + -14x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -6 + -14x + 16x2 = 0 + 14x + -14x + -16x2 + 16x2 -6 + -14x + 16x2 = 14x + -14x + -16x2 + 16x2 Combine like terms: 14x + -14x = 0 -6 + -14x + 16x2 = 0 + -16x2 + 16x2 -6 + -14x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6 + -14x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -7x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -7x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -7x + 8x2 = 0 Solving -3 + -7x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -0.875x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.875x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.875x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.875x + x2 = 0 + 0.375 -0.875x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.875x + x2 = 0.375 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 0.375 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 0.375 + 0.19140625 Combine like terms: 0.375 + 0.19140625 = 0.56640625 0.19140625 + -0.875x + x2 = 0.56640625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 0.56640625 Calculate the square root of the right side: 0.752599661 Break this problem into two subproblems by setting (x + -0.4375) equal to 0.752599661 and -0.752599661.Subproblem 1
x + -0.4375 = 0.752599661 Simplifying x + -0.4375 = 0.752599661 Reorder the terms: -0.4375 + x = 0.752599661 Solving -0.4375 + x = 0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 0.752599661 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 0.752599661 + 0.4375 x = 0.752599661 + 0.4375 Combine like terms: 0.752599661 + 0.4375 = 1.190099661 x = 1.190099661 Simplifying x = 1.190099661Subproblem 2
x + -0.4375 = -0.752599661 Simplifying x + -0.4375 = -0.752599661 Reorder the terms: -0.4375 + x = -0.752599661 Solving -0.4375 + x = -0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -0.752599661 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -0.752599661 + 0.4375 x = -0.752599661 + 0.4375 Combine like terms: -0.752599661 + 0.4375 = -0.315099661 x = -0.315099661 Simplifying x = -0.315099661Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.190099661, -0.315099661}Solution
x = {1.190099661, -0.315099661}
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