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Simplifying 2x2 + 40x = 800 Reorder the terms: 40x + 2x2 = 800 Solving 40x + 2x2 = 800 Solving for variable 'x'. Reorder the terms: -800 + 40x + 2x2 = 800 + -800 Combine like terms: 800 + -800 = 0 -800 + 40x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-400 + 20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-400 + 20x + x2)' equal to zero and attempt to solve: Simplifying -400 + 20x + x2 = 0 Solving -400 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 20x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 20x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 20x + x2 = 0 + 400 20x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 20x + x2 = 400 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 = 400 + 100 Reorder the terms: 100 + 20x + x2 = 400 + 100 Combine like terms: 400 + 100 = 500 100 + 20x + x2 = 500 Factor a perfect square on the left side: (x + 10)(x + 10) = 500 Calculate the square root of the right side: 22.360679775 Break this problem into two subproblems by setting (x + 10) equal to 22.360679775 and -22.360679775.Subproblem 1
x + 10 = 22.360679775 Simplifying x + 10 = 22.360679775 Reorder the terms: 10 + x = 22.360679775 Solving 10 + x = 22.360679775 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 = 22.360679775 + -10 Combine like terms: 10 + -10 = 0 0 + x = 22.360679775 + -10 x = 22.360679775 + -10 Combine like terms: 22.360679775 + -10 = 12.360679775 x = 12.360679775 Simplifying x = 12.360679775Subproblem 2
x + 10 = -22.360679775 Simplifying x + 10 = -22.360679775 Reorder the terms: 10 + x = -22.360679775 Solving 10 + x = -22.360679775 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 = -22.360679775 + -10 Combine like terms: 10 + -10 = 0 0 + x = -22.360679775 + -10 x = -22.360679775 + -10 Combine like terms: -22.360679775 + -10 = -32.360679775 x = -32.360679775 Simplifying x = -32.360679775Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.360679775, -32.360679775}Solution
x = {12.360679775, -32.360679775}
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