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Simplifying (5 + x)(8x) = 1220 Remove parenthesis around (8x) (5 + x) * 8x = 1220 Reorder the terms for easier multiplication: 8x(5 + x) = 1220 (5 * 8x + x * 8x) = 1220 (40x + 8x2) = 1220 Solving 40x + 8x2 = 1220 Solving for variable 'x'. Reorder the terms: -1220 + 40x + 8x2 = 1220 + -1220 Combine like terms: 1220 + -1220 = 0 -1220 + 40x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-305 + 10x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-305 + 10x + 2x2)' equal to zero and attempt to solve: Simplifying -305 + 10x + 2x2 = 0 Solving -305 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -152.5 + 5x + x2 = 0 Move the constant term to the right: Add '152.5' to each side of the equation. -152.5 + 5x + 152.5 + x2 = 0 + 152.5 Reorder the terms: -152.5 + 152.5 + 5x + x2 = 0 + 152.5 Combine like terms: -152.5 + 152.5 = 0.0 0.0 + 5x + x2 = 0 + 152.5 5x + x2 = 0 + 152.5 Combine like terms: 0 + 152.5 = 152.5 5x + x2 = 152.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 152.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 152.5 + 6.25 Combine like terms: 152.5 + 6.25 = 158.75 6.25 + 5x + x2 = 158.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 158.75 Calculate the square root of the right side: 12.599603168 Break this problem into two subproblems by setting (x + 2.5) equal to 12.599603168 and -12.599603168.Subproblem 1
x + 2.5 = 12.599603168 Simplifying x + 2.5 = 12.599603168 Reorder the terms: 2.5 + x = 12.599603168 Solving 2.5 + x = 12.599603168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 12.599603168 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.599603168 + -2.5 x = 12.599603168 + -2.5 Combine like terms: 12.599603168 + -2.5 = 10.099603168 x = 10.099603168 Simplifying x = 10.099603168Subproblem 2
x + 2.5 = -12.599603168 Simplifying x + 2.5 = -12.599603168 Reorder the terms: 2.5 + x = -12.599603168 Solving 2.5 + x = -12.599603168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -12.599603168 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.599603168 + -2.5 x = -12.599603168 + -2.5 Combine like terms: -12.599603168 + -2.5 = -15.099603168 x = -15.099603168 Simplifying x = -15.099603168Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.099603168, -15.099603168}Solution
x = {10.099603168, -15.099603168}
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