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Simplifying -2x(x + 8) = 4x + -34 Reorder the terms: -2x(8 + x) = 4x + -34 (8 * -2x + x * -2x) = 4x + -34 (-16x + -2x2) = 4x + -34 Reorder the terms: -16x + -2x2 = -34 + 4x Solving -16x + -2x2 = -34 + 4x Solving for variable 'x'. Reorder the terms: 34 + -16x + -4x + -2x2 = -34 + 4x + 34 + -4x Combine like terms: -16x + -4x = -20x 34 + -20x + -2x2 = -34 + 4x + 34 + -4x Reorder the terms: 34 + -20x + -2x2 = -34 + 34 + 4x + -4x Combine like terms: -34 + 34 = 0 34 + -20x + -2x2 = 0 + 4x + -4x 34 + -20x + -2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 34 + -20x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(17 + -10x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -10x + -1x2)' equal to zero and attempt to solve: Simplifying 17 + -10x + -1x2 = 0 Solving 17 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + 10x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 10x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 10x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 10x + x2 = 0 + 17 10x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 10x + x2 = 17 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 17 + 25 Reorder the terms: 25 + 10x + x2 = 17 + 25 Combine like terms: 17 + 25 = 42 25 + 10x + x2 = 42 Factor a perfect square on the left side: (x + 5)(x + 5) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + 5) equal to 6.480740698 and -6.480740698.Subproblem 1
x + 5 = 6.480740698 Simplifying x + 5 = 6.480740698 Reorder the terms: 5 + x = 6.480740698 Solving 5 + x = 6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.480740698 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.480740698 + -5 x = 6.480740698 + -5 Combine like terms: 6.480740698 + -5 = 1.480740698 x = 1.480740698 Simplifying x = 1.480740698Subproblem 2
x + 5 = -6.480740698 Simplifying x + 5 = -6.480740698 Reorder the terms: 5 + x = -6.480740698 Solving 5 + x = -6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.480740698 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.480740698 + -5 x = -6.480740698 + -5 Combine like terms: -6.480740698 + -5 = -11.480740698 x = -11.480740698 Simplifying x = -11.480740698Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.480740698, -11.480740698}Solution
x = {1.480740698, -11.480740698}
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