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Simplifying 82x + -1x2 = 150 Solving 82x + -1x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 82x + -1x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 82x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 150 + -82x + x2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + -82x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -82x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -82x + x2 = 0 + -150 -82x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -82x + x2 = -150 The x term is -82x. Take half its coefficient (-41). Square it (1681) and add it to both sides. Add '1681' to each side of the equation. -82x + 1681 + x2 = -150 + 1681 Reorder the terms: 1681 + -82x + x2 = -150 + 1681 Combine like terms: -150 + 1681 = 1531 1681 + -82x + x2 = 1531 Factor a perfect square on the left side: (x + -41)(x + -41) = 1531 Calculate the square root of the right side: 39.127995093 Break this problem into two subproblems by setting (x + -41) equal to 39.127995093 and -39.127995093.Subproblem 1
x + -41 = 39.127995093 Simplifying x + -41 = 39.127995093 Reorder the terms: -41 + x = 39.127995093 Solving -41 + x = 39.127995093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = 39.127995093 + 41 Combine like terms: -41 + 41 = 0 0 + x = 39.127995093 + 41 x = 39.127995093 + 41 Combine like terms: 39.127995093 + 41 = 80.127995093 x = 80.127995093 Simplifying x = 80.127995093Subproblem 2
x + -41 = -39.127995093 Simplifying x + -41 = -39.127995093 Reorder the terms: -41 + x = -39.127995093 Solving -41 + x = -39.127995093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = -39.127995093 + 41 Combine like terms: -41 + 41 = 0 0 + x = -39.127995093 + 41 x = -39.127995093 + 41 Combine like terms: -39.127995093 + 41 = 1.872004907 x = 1.872004907 Simplifying x = 1.872004907Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.127995093, 1.872004907}
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