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Simplifying 0 = 2x2 + -22x + -54 Reorder the terms: 0 = -54 + -22x + 2x2 Solving 0 = -54 + -22x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 54 = 54 54 + 22x + -2x2 = -54 + -22x + 2x2 + 54 + 22x + -2x2 Reorder the terms: 54 + 22x + -2x2 = -54 + 54 + -22x + 22x + 2x2 + -2x2 Combine like terms: -54 + 54 = 0 54 + 22x + -2x2 = 0 + -22x + 22x + 2x2 + -2x2 54 + 22x + -2x2 = -22x + 22x + 2x2 + -2x2 Combine like terms: -22x + 22x = 0 54 + 22x + -2x2 = 0 + 2x2 + -2x2 54 + 22x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 54 + 22x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 11x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + 11x + -1x2)' equal to zero and attempt to solve: Simplifying 27 + 11x + -1x2 = 0 Solving 27 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27 + -11x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -11x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -11x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -11x + x2 = 0 + 27 -11x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -11x + x2 = 27 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 27 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 27 + 30.25 Combine like terms: 27 + 30.25 = 57.25 30.25 + -11x + x2 = 57.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + -5.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + -5.5 = 7.566372975 Simplifying x + -5.5 = 7.566372975 Reorder the terms: -5.5 + x = 7.566372975 Solving -5.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 7.566372975 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.566372975 + 5.5 x = 7.566372975 + 5.5 Combine like terms: 7.566372975 + 5.5 = 13.066372975 x = 13.066372975 Simplifying x = 13.066372975Subproblem 2
x + -5.5 = -7.566372975 Simplifying x + -5.5 = -7.566372975 Reorder the terms: -5.5 + x = -7.566372975 Solving -5.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -7.566372975 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.566372975 + 5.5 x = -7.566372975 + 5.5 Combine like terms: -7.566372975 + 5.5 = -2.066372975 x = -2.066372975 Simplifying x = -2.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.066372975, -2.066372975}Solution
x = {13.066372975, -2.066372975}
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