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Simplifying 80x + -2x2 + 200 = 0 Reorder the terms: 200 + 80x + -2x2 = 0 Solving 200 + 80x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(100 + 40x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(100 + 40x + -1x2)' equal to zero and attempt to solve: Simplifying 100 + 40x + -1x2 = 0 Solving 100 + 40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + -40x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -40x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -40x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -40x + x2 = 0 + 100 -40x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -40x + x2 = 100 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 100 + 400 Reorder the terms: 400 + -40x + x2 = 100 + 400 Combine like terms: 100 + 400 = 500 400 + -40x + x2 = 500 Factor a perfect square on the left side: (x + -20)(x + -20) = 500 Calculate the square root of the right side: 22.360679775 Break this problem into two subproblems by setting (x + -20) equal to 22.360679775 and -22.360679775.Subproblem 1
x + -20 = 22.360679775 Simplifying x + -20 = 22.360679775 Reorder the terms: -20 + x = 22.360679775 Solving -20 + x = 22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 22.360679775 + 20 Combine like terms: -20 + 20 = 0 0 + x = 22.360679775 + 20 x = 22.360679775 + 20 Combine like terms: 22.360679775 + 20 = 42.360679775 x = 42.360679775 Simplifying x = 42.360679775Subproblem 2
x + -20 = -22.360679775 Simplifying x + -20 = -22.360679775 Reorder the terms: -20 + x = -22.360679775 Solving -20 + x = -22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -22.360679775 + 20 Combine like terms: -20 + 20 = 0 0 + x = -22.360679775 + 20 x = -22.360679775 + 20 Combine like terms: -22.360679775 + 20 = -2.360679775 x = -2.360679775 Simplifying x = -2.360679775Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.360679775, -2.360679775}Solution
x = {42.360679775, -2.360679775}
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