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Simplifying 0.5x2 + -11x + -36 = 0 Reorder the terms: -36 + -11x + 0.5x2 = 0 Solving -36 + -11x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -72 + -22x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + -22x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -22x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -22x + x2 = 0 + 72 -22x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -22x + x2 = 72 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = 72 + 121 Reorder the terms: 121 + -22x + x2 = 72 + 121 Combine like terms: 72 + 121 = 193 121 + -22x + x2 = 193 Factor a perfect square on the left side: (x + -11)(x + -11) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x + -11) equal to 13.892443989 and -13.892443989.Subproblem 1
x + -11 = 13.892443989 Simplifying x + -11 = 13.892443989 Reorder the terms: -11 + x = 13.892443989 Solving -11 + x = 13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 13.892443989 + 11 Combine like terms: -11 + 11 = 0 0 + x = 13.892443989 + 11 x = 13.892443989 + 11 Combine like terms: 13.892443989 + 11 = 24.892443989 x = 24.892443989 Simplifying x = 24.892443989Subproblem 2
x + -11 = -13.892443989 Simplifying x + -11 = -13.892443989 Reorder the terms: -11 + x = -13.892443989 Solving -11 + x = -13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -13.892443989 + 11 Combine like terms: -11 + 11 = 0 0 + x = -13.892443989 + 11 x = -13.892443989 + 11 Combine like terms: -13.892443989 + 11 = -2.892443989 x = -2.892443989 Simplifying x = -2.892443989Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.892443989, -2.892443989}
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