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Simplifying (40 + -2x)(30 + -2x) = 500 Multiply (40 + -2x) * (30 + -2x) (40(30 + -2x) + -2x * (30 + -2x)) = 500 ((30 * 40 + -2x * 40) + -2x * (30 + -2x)) = 500 ((1200 + -80x) + -2x * (30 + -2x)) = 500 (1200 + -80x + (30 * -2x + -2x * -2x)) = 500 (1200 + -80x + (-60x + 4x2)) = 500 Combine like terms: -80x + -60x = -140x (1200 + -140x + 4x2) = 500 Solving 1200 + -140x + 4x2 = 500 Solving for variable 'x'. Reorder the terms: 1200 + -500 + -140x + 4x2 = 500 + -500 Combine like terms: 1200 + -500 = 700 700 + -140x + 4x2 = 500 + -500 Combine like terms: 500 + -500 = 0 700 + -140x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(175 + -35x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(175 + -35x + x2)' equal to zero and attempt to solve: Simplifying 175 + -35x + x2 = 0 Solving 175 + -35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-175' to each side of the equation. 175 + -35x + -175 + x2 = 0 + -175 Reorder the terms: 175 + -175 + -35x + x2 = 0 + -175 Combine like terms: 175 + -175 = 0 0 + -35x + x2 = 0 + -175 -35x + x2 = 0 + -175 Combine like terms: 0 + -175 = -175 -35x + x2 = -175 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 = -175 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -175 + 306.25 Combine like terms: -175 + 306.25 = 131.25 306.25 + -35x + x2 = 131.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (x + -17.5) equal to 11.456439237 and -11.456439237.Subproblem 1
x + -17.5 = 11.456439237 Simplifying x + -17.5 = 11.456439237 Reorder the terms: -17.5 + x = 11.456439237 Solving -17.5 + x = 11.456439237 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 = 11.456439237 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 11.456439237 + 17.5 x = 11.456439237 + 17.5 Combine like terms: 11.456439237 + 17.5 = 28.956439237 x = 28.956439237 Simplifying x = 28.956439237Subproblem 2
x + -17.5 = -11.456439237 Simplifying x + -17.5 = -11.456439237 Reorder the terms: -17.5 + x = -11.456439237 Solving -17.5 + x = -11.456439237 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 = -11.456439237 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -11.456439237 + 17.5 x = -11.456439237 + 17.5 Combine like terms: -11.456439237 + 17.5 = 6.043560763 x = 6.043560763 Simplifying x = 6.043560763Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.956439237, 6.043560763}Solution
x = {28.956439237, 6.043560763}
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