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Simplifying 500x + -25x2 = 100 Solving 500x + -25x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 500x + -25x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 500x + -25x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(-4 + 20x + -1x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-4 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + 20x + -1x2 = 0 Solving -4 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -20x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -20x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -20x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -20x + x2 = 0 + -4 -20x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -20x + x2 = -4 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -4 + 100 Reorder the terms: 100 + -20x + x2 = -4 + 100 Combine like terms: -4 + 100 = 96 100 + -20x + x2 = 96 Factor a perfect square on the left side: (x + -10)(x + -10) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + -10) equal to 9.797958971 and -9.797958971.Subproblem 1
x + -10 = 9.797958971 Simplifying x + -10 = 9.797958971 Reorder the terms: -10 + x = 9.797958971 Solving -10 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.797958971 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.797958971 + 10 x = 9.797958971 + 10 Combine like terms: 9.797958971 + 10 = 19.797958971 x = 19.797958971 Simplifying x = 19.797958971Subproblem 2
x + -10 = -9.797958971 Simplifying x + -10 = -9.797958971 Reorder the terms: -10 + x = -9.797958971 Solving -10 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.797958971 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.797958971 + 10 x = -9.797958971 + 10 Combine like terms: -9.797958971 + 10 = 0.202041029 x = 0.202041029 Simplifying x = 0.202041029Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.797958971, 0.202041029}Solution
x = {19.797958971, 0.202041029}
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