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Simplifying (38 + -2x)(32 + -2x) = 600 Multiply (38 + -2x) * (32 + -2x) (38(32 + -2x) + -2x * (32 + -2x)) = 600 ((32 * 38 + -2x * 38) + -2x * (32 + -2x)) = 600 ((1216 + -76x) + -2x * (32 + -2x)) = 600 (1216 + -76x + (32 * -2x + -2x * -2x)) = 600 (1216 + -76x + (-64x + 4x2)) = 600 Combine like terms: -76x + -64x = -140x (1216 + -140x + 4x2) = 600 Solving 1216 + -140x + 4x2 = 600 Solving for variable 'x'. Reorder the terms: 1216 + -600 + -140x + 4x2 = 600 + -600 Combine like terms: 1216 + -600 = 616 616 + -140x + 4x2 = 600 + -600 Combine like terms: 600 + -600 = 0 616 + -140x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(154 + -35x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(154 + -35x + x2)' equal to zero and attempt to solve: Simplifying 154 + -35x + x2 = 0 Solving 154 + -35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-154' to each side of the equation. 154 + -35x + -154 + x2 = 0 + -154 Reorder the terms: 154 + -154 + -35x + x2 = 0 + -154 Combine like terms: 154 + -154 = 0 0 + -35x + x2 = 0 + -154 -35x + x2 = 0 + -154 Combine like terms: 0 + -154 = -154 -35x + x2 = -154 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -154 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -154 + 306.25 Combine like terms: -154 + 306.25 = 152.25 306.25 + -35x + x2 = 152.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 152.25 Calculate the square root of the right side: 12.338962679 Break this problem into two subproblems by setting (x + -17.5) equal to 12.338962679 and -12.338962679.Subproblem 1
x + -17.5 = 12.338962679 Simplifying x + -17.5 = 12.338962679 Reorder the terms: -17.5 + x = 12.338962679 Solving -17.5 + x = 12.338962679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 12.338962679 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 12.338962679 + 17.5 x = 12.338962679 + 17.5 Combine like terms: 12.338962679 + 17.5 = 29.838962679 x = 29.838962679 Simplifying x = 29.838962679Subproblem 2
x + -17.5 = -12.338962679 Simplifying x + -17.5 = -12.338962679 Reorder the terms: -17.5 + x = -12.338962679 Solving -17.5 + x = -12.338962679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -12.338962679 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -12.338962679 + 17.5 x = -12.338962679 + 17.5 Combine like terms: -12.338962679 + 17.5 = 5.161037321 x = 5.161037321 Simplifying x = 5.161037321Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.838962679, 5.161037321}Solution
x = {29.838962679, 5.161037321}
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