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Simplifying 7 + -2x + 16x2 = 13 Solving 7 + -2x + 16x2 = 13 Solving for variable 'x'. Reorder the terms: 7 + -13 + -2x + 16x2 = 13 + -13 Combine like terms: 7 + -13 = -6 -6 + -2x + 16x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -6 + -2x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -1x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -1x + 8x2 = 0 Solving -3 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.125x + x2 = 0 + 0.375 -0.125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.125x + x2 = 0.375 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 0.375 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.375 + 0.00390625 Combine like terms: 0.375 + 0.00390625 = 0.37890625 0.00390625 + -0.125x + x2 = 0.37890625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.37890625 Calculate the square root of the right side: 0.615553613 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.615553613 and -0.615553613.Subproblem 1
x + -0.0625 = 0.615553613 Simplifying x + -0.0625 = 0.615553613 Reorder the terms: -0.0625 + x = 0.615553613 Solving -0.0625 + x = 0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.615553613 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.615553613 + 0.0625 x = 0.615553613 + 0.0625 Combine like terms: 0.615553613 + 0.0625 = 0.678053613 x = 0.678053613 Simplifying x = 0.678053613Subproblem 2
x + -0.0625 = -0.615553613 Simplifying x + -0.0625 = -0.615553613 Reorder the terms: -0.0625 + x = -0.615553613 Solving -0.0625 + x = -0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.615553613 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.615553613 + 0.0625 x = -0.615553613 + 0.0625 Combine like terms: -0.615553613 + 0.0625 = -0.553053613 x = -0.553053613 Simplifying x = -0.553053613Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.678053613, -0.553053613}Solution
x = {0.678053613, -0.553053613}
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