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Simplifying 200 = 5x2 + -10x Reorder the terms: 200 = -10x + 5x2 Solving 200 = -10x + 5x2 Solving for variable 'x'. Reorder the terms: 200 + 10x + -5x2 = -10x + 10x + 5x2 + -5x2 Combine like terms: -10x + 10x = 0 200 + 10x + -5x2 = 0 + 5x2 + -5x2 200 + 10x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 200 + 10x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(40 + 2x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(40 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 40 + 2x + -1x2 = 0 Solving 40 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + -2x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -2x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -2x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -2x + x2 = 0 + 40 -2x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -2x + x2 = 40 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 40 + 1 Reorder the terms: 1 + -2x + x2 = 40 + 1 Combine like terms: 40 + 1 = 41 1 + -2x + x2 = 41 Factor a perfect square on the left side: (x + -1)(x + -1) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -1) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -1 = 6.403124237 Simplifying x + -1 = 6.403124237 Reorder the terms: -1 + x = 6.403124237 Solving -1 + x = 6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 6.403124237 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.403124237 + 1 x = 6.403124237 + 1 Combine like terms: 6.403124237 + 1 = 7.403124237 x = 7.403124237 Simplifying x = 7.403124237Subproblem 2
x + -1 = -6.403124237 Simplifying x + -1 = -6.403124237 Reorder the terms: -1 + x = -6.403124237 Solving -1 + x = -6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -6.403124237 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.403124237 + 1 x = -6.403124237 + 1 Combine like terms: -6.403124237 + 1 = -5.403124237 x = -5.403124237 Simplifying x = -5.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.403124237, -5.403124237}Solution
x = {7.403124237, -5.403124237}
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