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Simplifying 400x + -2x2 = 2500 Solving 400x + -2x2 = 2500 Solving for variable 'x'. Reorder the terms: -2500 + 400x + -2x2 = 2500 + -2500 Combine like terms: 2500 + -2500 = 0 -2500 + 400x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1250 + 200x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1250 + 200x + -1x2)' equal to zero and attempt to solve: Simplifying -1250 + 200x + -1x2 = 0 Solving -1250 + 200x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1250 + -200x + x2 = 0 Move the constant term to the right: Add '-1250' to each side of the equation. 1250 + -200x + -1250 + x2 = 0 + -1250 Reorder the terms: 1250 + -1250 + -200x + x2 = 0 + -1250 Combine like terms: 1250 + -1250 = 0 0 + -200x + x2 = 0 + -1250 -200x + x2 = 0 + -1250 Combine like terms: 0 + -1250 = -1250 -200x + x2 = -1250 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -1250 + 10000 Reorder the terms: 10000 + -200x + x2 = -1250 + 10000 Combine like terms: -1250 + 10000 = 8750 10000 + -200x + x2 = 8750 Factor a perfect square on the left side: (x + -100)(x + -100) = 8750 Calculate the square root of the right side: 93.541434669 Break this problem into two subproblems by setting (x + -100) equal to 93.541434669 and -93.541434669.Subproblem 1
x + -100 = 93.541434669 Simplifying x + -100 = 93.541434669 Reorder the terms: -100 + x = 93.541434669 Solving -100 + x = 93.541434669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 93.541434669 + 100 Combine like terms: -100 + 100 = 0 0 + x = 93.541434669 + 100 x = 93.541434669 + 100 Combine like terms: 93.541434669 + 100 = 193.541434669 x = 193.541434669 Simplifying x = 193.541434669Subproblem 2
x + -100 = -93.541434669 Simplifying x + -100 = -93.541434669 Reorder the terms: -100 + x = -93.541434669 Solving -100 + x = -93.541434669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -93.541434669 + 100 Combine like terms: -100 + 100 = 0 0 + x = -93.541434669 + 100 x = -93.541434669 + 100 Combine like terms: -93.541434669 + 100 = 6.458565331 x = 6.458565331 Simplifying x = 6.458565331Solution
The solution to the problem is based on the solutions from the subproblems. x = {193.541434669, 6.458565331}Solution
x = {193.541434669, 6.458565331}
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