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Simplifying 44x + -2x2 + -70 = 0 Reorder the terms: -70 + 44x + -2x2 = 0 Solving -70 + 44x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 22x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + 22x + -1x2)' equal to zero and attempt to solve: Simplifying -35 + 22x + -1x2 = 0 Solving -35 + 22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 35 + -22x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + -22x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -22x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -22x + x2 = 0 + -35 -22x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -22x + x2 = -35 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 = -35 + 121 Reorder the terms: 121 + -22x + x2 = -35 + 121 Combine like terms: -35 + 121 = 86 121 + -22x + x2 = 86 Factor a perfect square on the left side: (x + -11)(x + -11) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + -11) equal to 9.273618495 and -9.273618495.Subproblem 1
x + -11 = 9.273618495 Simplifying x + -11 = 9.273618495 Reorder the terms: -11 + x = 9.273618495 Solving -11 + x = 9.273618495 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 = 9.273618495 + 11 Combine like terms: -11 + 11 = 0 0 + x = 9.273618495 + 11 x = 9.273618495 + 11 Combine like terms: 9.273618495 + 11 = 20.273618495 x = 20.273618495 Simplifying x = 20.273618495Subproblem 2
x + -11 = -9.273618495 Simplifying x + -11 = -9.273618495 Reorder the terms: -11 + x = -9.273618495 Solving -11 + x = -9.273618495 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 = -9.273618495 + 11 Combine like terms: -11 + 11 = 0 0 + x = -9.273618495 + 11 x = -9.273618495 + 11 Combine like terms: -9.273618495 + 11 = 1.726381505 x = 1.726381505 Simplifying x = 1.726381505Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.273618495, 1.726381505}Solution
x = {20.273618495, 1.726381505}
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