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Simplifying (34 + -2x)(21 + -2x) = 600 Multiply (34 + -2x) * (21 + -2x) (34(21 + -2x) + -2x * (21 + -2x)) = 600 ((21 * 34 + -2x * 34) + -2x * (21 + -2x)) = 600 ((714 + -68x) + -2x * (21 + -2x)) = 600 (714 + -68x + (21 * -2x + -2x * -2x)) = 600 (714 + -68x + (-42x + 4x2)) = 600 Combine like terms: -68x + -42x = -110x (714 + -110x + 4x2) = 600 Solving 714 + -110x + 4x2 = 600 Solving for variable 'x'. Reorder the terms: 714 + -600 + -110x + 4x2 = 600 + -600 Combine like terms: 714 + -600 = 114 114 + -110x + 4x2 = 600 + -600 Combine like terms: 600 + -600 = 0 114 + -110x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(57 + -55x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(57 + -55x + 2x2)' equal to zero and attempt to solve: Simplifying 57 + -55x + 2x2 = 0 Solving 57 + -55x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 28.5 + -27.5x + x2 = 0 Move the constant term to the right: Add '-28.5' to each side of the equation. 28.5 + -27.5x + -28.5 + x2 = 0 + -28.5 Reorder the terms: 28.5 + -28.5 + -27.5x + x2 = 0 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + -27.5x + x2 = 0 + -28.5 -27.5x + x2 = 0 + -28.5 Combine like terms: 0 + -28.5 = -28.5 -27.5x + x2 = -28.5 The x term is -27.5x. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5x + 189.0625 + x2 = -28.5 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = -28.5 + 189.0625 Combine like terms: -28.5 + 189.0625 = 160.5625 189.0625 + -27.5x + x2 = 160.5625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 160.5625 Calculate the square root of the right side: 12.671325897 Break this problem into two subproblems by setting (x + -13.75) equal to 12.671325897 and -12.671325897.Subproblem 1
x + -13.75 = 12.671325897 Simplifying x + -13.75 = 12.671325897 Reorder the terms: -13.75 + x = 12.671325897 Solving -13.75 + x = 12.671325897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = 12.671325897 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 12.671325897 + 13.75 x = 12.671325897 + 13.75 Combine like terms: 12.671325897 + 13.75 = 26.421325897 x = 26.421325897 Simplifying x = 26.421325897Subproblem 2
x + -13.75 = -12.671325897 Simplifying x + -13.75 = -12.671325897 Reorder the terms: -13.75 + x = -12.671325897 Solving -13.75 + x = -12.671325897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = -12.671325897 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -12.671325897 + 13.75 x = -12.671325897 + 13.75 Combine like terms: -12.671325897 + 13.75 = 1.078674103 x = 1.078674103 Simplifying x = 1.078674103Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.421325897, 1.078674103}Solution
x = {26.421325897, 1.078674103}
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