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Simplifying 0 = -16x2 + 62x + 4 Reorder the terms: 0 = 4 + 62x + -16x2 Solving 0 = 4 + 62x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -62x + 16x2 = 4 + 62x + -16x2 + -4 + -62x + 16x2 Reorder the terms: -4 + -62x + 16x2 = 4 + -4 + 62x + -62x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 -4 + -62x + 16x2 = 0 + 62x + -62x + -16x2 + 16x2 -4 + -62x + 16x2 = 62x + -62x + -16x2 + 16x2 Combine like terms: 62x + -62x = 0 -4 + -62x + 16x2 = 0 + -16x2 + 16x2 -4 + -62x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -4 + -62x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -31x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -31x + 8x2)' equal to zero and attempt to solve: Simplifying -2 + -31x + 8x2 = 0 Solving -2 + -31x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -3.875x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -3.875x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -3.875x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -3.875x + x2 = 0 + 0.25 -3.875x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -3.875x + x2 = 0.25 The x term is -3.875x. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875x + 3.75390625 + x2 = 0.25 + 3.75390625 Reorder the terms: 3.75390625 + -3.875x + x2 = 0.25 + 3.75390625 Combine like terms: 0.25 + 3.75390625 = 4.00390625 3.75390625 + -3.875x + x2 = 4.00390625 Factor a perfect square on the left side: (x + -1.9375)(x + -1.9375) = 4.00390625 Calculate the square root of the right side: 2.000976324 Break this problem into two subproblems by setting (x + -1.9375) equal to 2.000976324 and -2.000976324.Subproblem 1
x + -1.9375 = 2.000976324 Simplifying x + -1.9375 = 2.000976324 Reorder the terms: -1.9375 + x = 2.000976324 Solving -1.9375 + x = 2.000976324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = 2.000976324 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = 2.000976324 + 1.9375 x = 2.000976324 + 1.9375 Combine like terms: 2.000976324 + 1.9375 = 3.938476324 x = 3.938476324 Simplifying x = 3.938476324Subproblem 2
x + -1.9375 = -2.000976324 Simplifying x + -1.9375 = -2.000976324 Reorder the terms: -1.9375 + x = -2.000976324 Solving -1.9375 + x = -2.000976324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = -2.000976324 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = -2.000976324 + 1.9375 x = -2.000976324 + 1.9375 Combine like terms: -2.000976324 + 1.9375 = -0.063476324 x = -0.063476324 Simplifying x = -0.063476324Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.938476324, -0.063476324}Solution
x = {3.938476324, -0.063476324}
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