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Simplifying 200 = (50 + -2x)(20 + -2x) Multiply (50 + -2x) * (20 + -2x) 200 = (50(20 + -2x) + -2x * (20 + -2x)) 200 = ((20 * 50 + -2x * 50) + -2x * (20 + -2x)) 200 = ((1000 + -100x) + -2x * (20 + -2x)) 200 = (1000 + -100x + (20 * -2x + -2x * -2x)) 200 = (1000 + -100x + (-40x + 4x2)) Combine like terms: -100x + -40x = -140x 200 = (1000 + -140x + 4x2) Solving 200 = 1000 + -140x + 4x2 Solving for variable 'x'. Combine like terms: 200 + -1000 = -800 -800 + 140x + -4x2 = 1000 + -140x + 4x2 + -1000 + 140x + -4x2 Reorder the terms: -800 + 140x + -4x2 = 1000 + -1000 + -140x + 140x + 4x2 + -4x2 Combine like terms: 1000 + -1000 = 0 -800 + 140x + -4x2 = 0 + -140x + 140x + 4x2 + -4x2 -800 + 140x + -4x2 = -140x + 140x + 4x2 + -4x2 Combine like terms: -140x + 140x = 0 -800 + 140x + -4x2 = 0 + 4x2 + -4x2 -800 + 140x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -800 + 140x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-200 + 35x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-200 + 35x + -1x2)' equal to zero and attempt to solve: Simplifying -200 + 35x + -1x2 = 0 Solving -200 + 35x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 200 + -35x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -35x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -35x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -35x + x2 = 0 + -200 -35x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -35x + x2 = -200 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 = -200 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -200 + 306.25 Combine like terms: -200 + 306.25 = 106.25 306.25 + -35x + x2 = 106.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + -17.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + -17.5 = 10.307764064 Simplifying x + -17.5 = 10.307764064 Reorder the terms: -17.5 + x = 10.307764064 Solving -17.5 + x = 10.307764064 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 = 10.307764064 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 10.307764064 + 17.5 x = 10.307764064 + 17.5 Combine like terms: 10.307764064 + 17.5 = 27.807764064 x = 27.807764064 Simplifying x = 27.807764064Subproblem 2
x + -17.5 = -10.307764064 Simplifying x + -17.5 = -10.307764064 Reorder the terms: -17.5 + x = -10.307764064 Solving -17.5 + x = -10.307764064 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 = -10.307764064 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -10.307764064 + 17.5 x = -10.307764064 + 17.5 Combine like terms: -10.307764064 + 17.5 = 7.192235936 x = 7.192235936 Simplifying x = 7.192235936Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.807764064, 7.192235936}Solution
x = {27.807764064, 7.192235936}
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