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Simplifying 0 = 16x2 + 14x + 2 Reorder the terms: 0 = 2 + 14x + 16x2 Solving 0 = 2 + 14x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -14x + -16x2 = 2 + 14x + 16x2 + -2 + -14x + -16x2 Reorder the terms: -2 + -14x + -16x2 = 2 + -2 + 14x + -14x + 16x2 + -16x2 Combine like terms: 2 + -2 = 0 -2 + -14x + -16x2 = 0 + 14x + -14x + 16x2 + -16x2 -2 + -14x + -16x2 = 14x + -14x + 16x2 + -16x2 Combine like terms: 14x + -14x = 0 -2 + -14x + -16x2 = 0 + 16x2 + -16x2 -2 + -14x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -2 + -14x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + 7x + 8x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1 + 7x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + 7x + 8x2 = 0 Solving 1 + 7x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 0.875x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 0.875x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 0.875x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 0.875x + x2 = 0 + -0.125 0.875x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 0.875x + x2 = -0.125 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 = -0.125 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = -0.125 + 0.19140625 Combine like terms: -0.125 + 0.19140625 = 0.06640625 0.19140625 + 0.875x + x2 = 0.06640625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (x + 0.4375) equal to 0.257694102 and -0.257694102.Subproblem 1
x + 0.4375 = 0.257694102 Simplifying x + 0.4375 = 0.257694102 Reorder the terms: 0.4375 + x = 0.257694102 Solving 0.4375 + x = 0.257694102 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 = 0.257694102 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 0.257694102 + -0.4375 x = 0.257694102 + -0.4375 Combine like terms: 0.257694102 + -0.4375 = -0.179805898 x = -0.179805898 Simplifying x = -0.179805898Subproblem 2
x + 0.4375 = -0.257694102 Simplifying x + 0.4375 = -0.257694102 Reorder the terms: 0.4375 + x = -0.257694102 Solving 0.4375 + x = -0.257694102 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 = -0.257694102 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -0.257694102 + -0.4375 x = -0.257694102 + -0.4375 Combine like terms: -0.257694102 + -0.4375 = -0.695194102 x = -0.695194102 Simplifying x = -0.695194102Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.179805898, -0.695194102}Solution
x = {-0.179805898, -0.695194102}
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