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Simplifying 0 = -2x2 + 40x + -82 Reorder the terms: 0 = -82 + 40x + -2x2 Solving 0 = -82 + 40x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 82 = 82 82 + -40x + 2x2 = -82 + 40x + -2x2 + 82 + -40x + 2x2 Reorder the terms: 82 + -40x + 2x2 = -82 + 82 + 40x + -40x + -2x2 + 2x2 Combine like terms: -82 + 82 = 0 82 + -40x + 2x2 = 0 + 40x + -40x + -2x2 + 2x2 82 + -40x + 2x2 = 40x + -40x + -2x2 + 2x2 Combine like terms: 40x + -40x = 0 82 + -40x + 2x2 = 0 + -2x2 + 2x2 82 + -40x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 82 + -40x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(41 + -20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + -20x + x2)' equal to zero and attempt to solve: Simplifying 41 + -20x + x2 = 0 Solving 41 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -20x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -20x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -20x + x2 = 0 + -41 -20x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -20x + x2 = -41 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 = -41 + 100 Reorder the terms: 100 + -20x + x2 = -41 + 100 Combine like terms: -41 + 100 = 59 100 + -20x + x2 = 59 Factor a perfect square on the left side: (x + -10)(x + -10) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + -10) equal to 7.681145748 and -7.681145748.Subproblem 1
x + -10 = 7.681145748 Simplifying x + -10 = 7.681145748 Reorder the terms: -10 + x = 7.681145748 Solving -10 + x = 7.681145748 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 = 7.681145748 + 10 Combine like terms: -10 + 10 = 0 0 + x = 7.681145748 + 10 x = 7.681145748 + 10 Combine like terms: 7.681145748 + 10 = 17.681145748 x = 17.681145748 Simplifying x = 17.681145748Subproblem 2
x + -10 = -7.681145748 Simplifying x + -10 = -7.681145748 Reorder the terms: -10 + x = -7.681145748 Solving -10 + x = -7.681145748 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 = -7.681145748 + 10 Combine like terms: -10 + 10 = 0 0 + x = -7.681145748 + 10 x = -7.681145748 + 10 Combine like terms: -7.681145748 + 10 = 2.318854252 x = 2.318854252 Simplifying x = 2.318854252Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.681145748, 2.318854252}Solution
x = {17.681145748, 2.318854252}
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