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Simplifying (4x2) + -80x + 397 = 0 Reorder the terms: 397 + -80x + (4x2) = 0 Solving 397 + -80x + (4x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 99.25 + -20x + x2 = 0 Move the constant term to the right: Add '-99.25' to each side of the equation. 99.25 + -20x + -99.25 + x2 = 0 + -99.25 Reorder the terms: 99.25 + -99.25 + -20x + x2 = 0 + -99.25 Combine like terms: 99.25 + -99.25 = 0.00 0.00 + -20x + x2 = 0 + -99.25 -20x + x2 = 0 + -99.25 Combine like terms: 0 + -99.25 = -99.25 -20x + x2 = -99.25 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 = -99.25 + 100 Reorder the terms: 100 + -20x + x2 = -99.25 + 100 Combine like terms: -99.25 + 100 = 0.75 100 + -20x + x2 = 0.75 Factor a perfect square on the left side: ((x) + -10)((x) + -10) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting ((x) + -10) equal to 0.866025404 and -0.866025404.Subproblem 1
(x) + -10 = 0.866025404 Simplifying (x) + -10 = 0.866025404 x + -10 = 0.866025404 Reorder the terms: -10 + x = 0.866025404 Solving -10 + x = 0.866025404 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 = 0.866025404 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0.866025404 + 10 x = 0.866025404 + 10 Combine like terms: 0.866025404 + 10 = 10.866025404 x = 10.866025404 Simplifying x = 10.866025404Subproblem 2
(x) + -10 = -0.866025404 Simplifying (x) + -10 = -0.866025404 x + -10 = -0.866025404 Reorder the terms: -10 + x = -0.866025404 Solving -10 + x = -0.866025404 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 = -0.866025404 + 10 Combine like terms: -10 + 10 = 0 0 + x = -0.866025404 + 10 x = -0.866025404 + 10 Combine like terms: -0.866025404 + 10 = 9.133974596 x = 9.133974596 Simplifying x = 9.133974596Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.866025404, 9.133974596}
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