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Simplifying (x + 13)(-2x + 2) + -24x = 0 Reorder the terms: (13 + x)(-2x + 2) + -24x = 0 Reorder the terms: (13 + x)(2 + -2x) + -24x = 0 Multiply (13 + x) * (2 + -2x) (13(2 + -2x) + x(2 + -2x)) + -24x = 0 ((2 * 13 + -2x * 13) + x(2 + -2x)) + -24x = 0 ((26 + -26x) + x(2 + -2x)) + -24x = 0 (26 + -26x + (2 * x + -2x * x)) + -24x = 0 (26 + -26x + (2x + -2x2)) + -24x = 0 Combine like terms: -26x + 2x = -24x (26 + -24x + -2x2) + -24x = 0 Reorder the terms: 26 + -24x + -24x + -2x2 = 0 Combine like terms: -24x + -24x = -48x 26 + -48x + -2x2 = 0 Solving 26 + -48x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -24x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -24x + -1x2)' equal to zero and attempt to solve: Simplifying 13 + -24x + -1x2 = 0 Solving 13 + -24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + 24x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 24x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 24x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 24x + x2 = 0 + 13 24x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 24x + x2 = 13 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 13 + 144 Reorder the terms: 144 + 24x + x2 = 13 + 144 Combine like terms: 13 + 144 = 157 144 + 24x + x2 = 157 Factor a perfect square on the left side: (x + 12)(x + 12) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (x + 12) equal to 12.529964086 and -12.529964086.Subproblem 1
x + 12 = 12.529964086 Simplifying x + 12 = 12.529964086 Reorder the terms: 12 + x = 12.529964086 Solving 12 + x = 12.529964086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 12.529964086 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.529964086 + -12 x = 12.529964086 + -12 Combine like terms: 12.529964086 + -12 = 0.529964086 x = 0.529964086 Simplifying x = 0.529964086Subproblem 2
x + 12 = -12.529964086 Simplifying x + 12 = -12.529964086 Reorder the terms: 12 + x = -12.529964086 Solving 12 + x = -12.529964086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -12.529964086 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.529964086 + -12 x = -12.529964086 + -12 Combine like terms: -12.529964086 + -12 = -24.529964086 x = -24.529964086 Simplifying x = -24.529964086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.529964086, -24.529964086}Solution
x = {0.529964086, -24.529964086}
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