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Simplifying 0 = (-16x2) + 112x + 28 Reorder the terms: 0 = 28 + 112x + (-16x2) Solving 0 = 28 + 112x + (-16x2) Solving for variable 'x'. Combine like terms: 0 + -28 = -28 -28 + -112x + (16x2) = 28 + 112x + (-16x2) + -28 + -112x + (16x2) Reorder the terms: -28 + -112x + (16x2) = 28 + -28 + 112x + -112x + (-16x2) + (16x2) Combine like terms: 28 + -28 = 0 -28 + -112x + (16x2) = 0 + 112x + -112x + (-16x2) + (16x2) -28 + -112x + (16x2) = 112x + -112x + (-16x2) + (16x2) Combine like terms: 112x + -112x = 0 -28 + -112x + (16x2) = 0 + (-16x2) + (16x2) -28 + -112x + (16x2) = (-16x2) + (16x2) Combine like terms: (-16x2) + (16x2) = 0 -28 + -112x + (16x2) = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + -28x + (4x2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -28x + (4x2))' equal to zero and attempt to solve: Simplifying -7 + -28x + (4x2) = 0 Solving -7 + -28x + (4x2) = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -7x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -7x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -7x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -7x + x2 = 0 + 1.75 -7x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -7x + x2 = 1.75 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 = 1.75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 1.75 + 12.25 Combine like terms: 1.75 + 12.25 = 14 12.25 + -7x + x2 = 14 Factor a perfect square on the left side: ((x) + -3.5)((x) + -3.5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting ((x) + -3.5) equal to 3.741657387 and -3.741657387.Subproblem 1
(x) + -3.5 = 3.741657387 Simplifying (x) + -3.5 = 3.741657387 x + -3.5 = 3.741657387 Reorder the terms: -3.5 + x = 3.741657387 Solving -3.5 + x = 3.741657387 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 = 3.741657387 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.741657387 + 3.5 x = 3.741657387 + 3.5 Combine like terms: 3.741657387 + 3.5 = 7.241657387 x = 7.241657387 Simplifying x = 7.241657387Subproblem 2
(x) + -3.5 = -3.741657387 Simplifying (x) + -3.5 = -3.741657387 x + -3.5 = -3.741657387 Reorder the terms: -3.5 + x = -3.741657387 Solving -3.5 + x = -3.741657387 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 = -3.741657387 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.741657387 + 3.5 x = -3.741657387 + 3.5 Combine like terms: -3.741657387 + 3.5 = -0.241657387 x = -0.241657387 Simplifying x = -0.241657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.241657387, -0.241657387}Solution
x = {7.241657387, -0.241657387}
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