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Simplifying -2x2 + -44x = -10 Reorder the terms: -44x + -2x2 = -10 Solving -44x + -2x2 = -10 Solving for variable 'x'. Reorder the terms: 10 + -44x + -2x2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -44x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -22x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -22x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -22x + -1x2 = 0 Solving 5 + -22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 22x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 22x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 22x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 22x + x2 = 0 + 5 22x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 22x + x2 = 5 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 = 5 + 121 Reorder the terms: 121 + 22x + x2 = 5 + 121 Combine like terms: 5 + 121 = 126 121 + 22x + x2 = 126 Factor a perfect square on the left side: (x + 11)(x + 11) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + 11) equal to 11.22497216 and -11.22497216.Subproblem 1
x + 11 = 11.22497216 Simplifying x + 11 = 11.22497216 Reorder the terms: 11 + x = 11.22497216 Solving 11 + x = 11.22497216 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 = 11.22497216 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.22497216 + -11 x = 11.22497216 + -11 Combine like terms: 11.22497216 + -11 = 0.22497216 x = 0.22497216 Simplifying x = 0.22497216Subproblem 2
x + 11 = -11.22497216 Simplifying x + 11 = -11.22497216 Reorder the terms: 11 + x = -11.22497216 Solving 11 + x = -11.22497216 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 = -11.22497216 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.22497216 + -11 x = -11.22497216 + -11 Combine like terms: -11.22497216 + -11 = -22.22497216 x = -22.22497216 Simplifying x = -22.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.22497216, -22.22497216}Solution
x = {0.22497216, -22.22497216}
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