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Simplifying 0 = -16x2 + 112x + 40 Reorder the terms: 0 = 40 + 112x + -16x2 Solving 0 = 40 + 112x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + -112x + 16x2 = 40 + 112x + -16x2 + -40 + -112x + 16x2 Reorder the terms: -40 + -112x + 16x2 = 40 + -40 + 112x + -112x + -16x2 + 16x2 Combine like terms: 40 + -40 = 0 -40 + -112x + 16x2 = 0 + 112x + -112x + -16x2 + 16x2 -40 + -112x + 16x2 = 112x + -112x + -16x2 + 16x2 Combine like terms: 112x + -112x = 0 -40 + -112x + 16x2 = 0 + -16x2 + 16x2 -40 + -112x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -40 + -112x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + -14x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + -14x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + -14x + 2x2 = 0 Solving -5 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -7x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -7x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -7x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -7x + x2 = 0 + 2.5 -7x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -7x + x2 = 2.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 2.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 2.5 + 12.25 Combine like terms: 2.5 + 12.25 = 14.75 12.25 + -7x + x2 = 14.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (x + -3.5) equal to 3.840572874 and -3.840572874.Subproblem 1
x + -3.5 = 3.840572874 Simplifying x + -3.5 = 3.840572874 Reorder the terms: -3.5 + x = 3.840572874 Solving -3.5 + x = 3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.840572874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.840572874 + 3.5 x = 3.840572874 + 3.5 Combine like terms: 3.840572874 + 3.5 = 7.340572874 x = 7.340572874 Simplifying x = 7.340572874Subproblem 2
x + -3.5 = -3.840572874 Simplifying x + -3.5 = -3.840572874 Reorder the terms: -3.5 + x = -3.840572874 Solving -3.5 + x = -3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.840572874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.840572874 + 3.5 x = -3.840572874 + 3.5 Combine like terms: -3.840572874 + 3.5 = -0.340572874 x = -0.340572874 Simplifying x = -0.340572874Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.340572874, -0.340572874}Solution
x = {7.340572874, -0.340572874}
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