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Simplifying (200 + -2x)(80 + -2x) = 10000 Multiply (200 + -2x) * (80 + -2x) (200(80 + -2x) + -2x * (80 + -2x)) = 10000 ((80 * 200 + -2x * 200) + -2x * (80 + -2x)) = 10000 ((16000 + -400x) + -2x * (80 + -2x)) = 10000 (16000 + -400x + (80 * -2x + -2x * -2x)) = 10000 (16000 + -400x + (-160x + 4x2)) = 10000 Combine like terms: -400x + -160x = -560x (16000 + -560x + 4x2) = 10000 Solving 16000 + -560x + 4x2 = 10000 Solving for variable 'x'. Reorder the terms: 16000 + -10000 + -560x + 4x2 = 10000 + -10000 Combine like terms: 16000 + -10000 = 6000 6000 + -560x + 4x2 = 10000 + -10000 Combine like terms: 10000 + -10000 = 0 6000 + -560x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1500 + -140x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1500 + -140x + x2)' equal to zero and attempt to solve: Simplifying 1500 + -140x + x2 = 0 Solving 1500 + -140x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1500' to each side of the equation. 1500 + -140x + -1500 + x2 = 0 + -1500 Reorder the terms: 1500 + -1500 + -140x + x2 = 0 + -1500 Combine like terms: 1500 + -1500 = 0 0 + -140x + x2 = 0 + -1500 -140x + x2 = 0 + -1500 Combine like terms: 0 + -1500 = -1500 -140x + x2 = -1500 The x term is -140x. Take half its coefficient (-70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. -140x + 4900 + x2 = -1500 + 4900 Reorder the terms: 4900 + -140x + x2 = -1500 + 4900 Combine like terms: -1500 + 4900 = 3400 4900 + -140x + x2 = 3400 Factor a perfect square on the left side: (x + -70)(x + -70) = 3400 Calculate the square root of the right side: 58.309518948 Break this problem into two subproblems by setting (x + -70) equal to 58.309518948 and -58.309518948.Subproblem 1
x + -70 = 58.309518948 Simplifying x + -70 = 58.309518948 Reorder the terms: -70 + x = 58.309518948 Solving -70 + x = 58.309518948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = 58.309518948 + 70 Combine like terms: -70 + 70 = 0 0 + x = 58.309518948 + 70 x = 58.309518948 + 70 Combine like terms: 58.309518948 + 70 = 128.309518948 x = 128.309518948 Simplifying x = 128.309518948Subproblem 2
x + -70 = -58.309518948 Simplifying x + -70 = -58.309518948 Reorder the terms: -70 + x = -58.309518948 Solving -70 + x = -58.309518948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = -58.309518948 + 70 Combine like terms: -70 + 70 = 0 0 + x = -58.309518948 + 70 x = -58.309518948 + 70 Combine like terms: -58.309518948 + 70 = 11.690481052 x = 11.690481052 Simplifying x = 11.690481052Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.309518948, 11.690481052}Solution
x = {128.309518948, 11.690481052}
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