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Simplifying 24(42) = (x + 8) * 2x + -4 Multiply 24 * 42 1008 = (x + 8) * 2x + -4 Reorder the terms: 1008 = (8 + x) * 2x + -4 Reorder the terms for easier multiplication: 1008 = 2x(8 + x) + -4 1008 = (8 * 2x + x * 2x) + -4 1008 = (16x + 2x2) + -4 Reorder the terms: 1008 = -4 + 16x + 2x2 Solving 1008 = -4 + 16x + 2x2 Solving for variable 'x'. Combine like terms: 1008 + 4 = 1012 1012 + -16x + -2x2 = -4 + 16x + 2x2 + 4 + -16x + -2x2 Reorder the terms: 1012 + -16x + -2x2 = -4 + 4 + 16x + -16x + 2x2 + -2x2 Combine like terms: -4 + 4 = 0 1012 + -16x + -2x2 = 0 + 16x + -16x + 2x2 + -2x2 1012 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 1012 + -16x + -2x2 = 0 + 2x2 + -2x2 1012 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1012 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(506 + -8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(506 + -8x + -1x2)' equal to zero and attempt to solve: Simplifying 506 + -8x + -1x2 = 0 Solving 506 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -506 + 8x + x2 = 0 Move the constant term to the right: Add '506' to each side of the equation. -506 + 8x + 506 + x2 = 0 + 506 Reorder the terms: -506 + 506 + 8x + x2 = 0 + 506 Combine like terms: -506 + 506 = 0 0 + 8x + x2 = 0 + 506 8x + x2 = 0 + 506 Combine like terms: 0 + 506 = 506 8x + x2 = 506 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 506 + 16 Reorder the terms: 16 + 8x + x2 = 506 + 16 Combine like terms: 506 + 16 = 522 16 + 8x + x2 = 522 Factor a perfect square on the left side: (x + 4)(x + 4) = 522 Calculate the square root of the right side: 22.847319318 Break this problem into two subproblems by setting (x + 4) equal to 22.847319318 and -22.847319318.Subproblem 1
x + 4 = 22.847319318 Simplifying x + 4 = 22.847319318 Reorder the terms: 4 + x = 22.847319318 Solving 4 + x = 22.847319318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 22.847319318 + -4 Combine like terms: 4 + -4 = 0 0 + x = 22.847319318 + -4 x = 22.847319318 + -4 Combine like terms: 22.847319318 + -4 = 18.847319318 x = 18.847319318 Simplifying x = 18.847319318Subproblem 2
x + 4 = -22.847319318 Simplifying x + 4 = -22.847319318 Reorder the terms: 4 + x = -22.847319318 Solving 4 + x = -22.847319318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -22.847319318 + -4 Combine like terms: 4 + -4 = 0 0 + x = -22.847319318 + -4 x = -22.847319318 + -4 Combine like terms: -22.847319318 + -4 = -26.847319318 x = -26.847319318 Simplifying x = -26.847319318Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.847319318, -26.847319318}Solution
x = {18.847319318, -26.847319318}
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