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Simplifying 336 = (8 + 2x)(10 + 2x) + -1(8)(10) Multiply (8 + 2x) * (10 + 2x) 336 = (8(10 + 2x) + 2x * (10 + 2x)) + -1(8)(10) 336 = ((10 * 8 + 2x * 8) + 2x * (10 + 2x)) + -1(8)(10) 336 = ((80 + 16x) + 2x * (10 + 2x)) + -1(8)(10) 336 = (80 + 16x + (10 * 2x + 2x * 2x)) + -1(8)(10) 336 = (80 + 16x + (20x + 4x2)) + -1(8)(10) Combine like terms: 16x + 20x = 36x 336 = (80 + 36x + 4x2) + -1(8)(10) Multiply -1 * 8 336 = 80 + 36x + 4x2 + -8 * 10 Multiply -8 * 10 336 = 80 + 36x + 4x2 + -80 Reorder the terms: 336 = 80 + -80 + 36x + 4x2 Combine like terms: 80 + -80 = 0 336 = 0 + 36x + 4x2 336 = 36x + 4x2 Solving 336 = 36x + 4x2 Solving for variable 'x'. Reorder the terms: 336 + -36x + -4x2 = 36x + -36x + 4x2 + -4x2 Combine like terms: 36x + -36x = 0 336 + -36x + -4x2 = 0 + 4x2 + -4x2 336 + -36x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 336 + -36x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(84 + -9x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(84 + -9x + -1x2)' equal to zero and attempt to solve: Simplifying 84 + -9x + -1x2 = 0 Solving 84 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -84 + 9x + x2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + 9x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 9x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 9x + x2 = 0 + 84 9x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 9x + x2 = 84 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 84 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 84 + 20.25 Combine like terms: 84 + 20.25 = 104.25 20.25 + 9x + x2 = 104.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (x + 4.5) equal to 10.210288928 and -10.210288928.Subproblem 1
x + 4.5 = 10.210288928 Simplifying x + 4.5 = 10.210288928 Reorder the terms: 4.5 + x = 10.210288928 Solving 4.5 + x = 10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 10.210288928 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 10.210288928 + -4.5 x = 10.210288928 + -4.5 Combine like terms: 10.210288928 + -4.5 = 5.710288928 x = 5.710288928 Simplifying x = 5.710288928Subproblem 2
x + 4.5 = -10.210288928 Simplifying x + 4.5 = -10.210288928 Reorder the terms: 4.5 + x = -10.210288928 Solving 4.5 + x = -10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -10.210288928 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -10.210288928 + -4.5 x = -10.210288928 + -4.5 Combine like terms: -10.210288928 + -4.5 = -14.710288928 x = -14.710288928 Simplifying x = -14.710288928Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.710288928, -14.710288928}Solution
x = {5.710288928, -14.710288928}
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