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Simplifying 2x2 + -22x + 28 = 117 Reorder the terms: 28 + -22x + 2x2 = 117 Solving 28 + -22x + 2x2 = 117 Solving for variable 'x'. Reorder the terms: 28 + -117 + -22x + 2x2 = 117 + -117 Combine like terms: 28 + -117 = -89 -89 + -22x + 2x2 = 117 + -117 Combine like terms: 117 + -117 = 0 -89 + -22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -44.5 + -11x + x2 = 0 Move the constant term to the right: Add '44.5' to each side of the equation. -44.5 + -11x + 44.5 + x2 = 0 + 44.5 Reorder the terms: -44.5 + 44.5 + -11x + x2 = 0 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + -11x + x2 = 0 + 44.5 -11x + x2 = 0 + 44.5 Combine like terms: 0 + 44.5 = 44.5 -11x + x2 = 44.5 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 = 44.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 44.5 + 30.25 Combine like terms: 44.5 + 30.25 = 74.75 30.25 + -11x + x2 = 74.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 74.75 Calculate the square root of the right side: 8.645808233 Break this problem into two subproblems by setting (x + -5.5) equal to 8.645808233 and -8.645808233.Subproblem 1
x + -5.5 = 8.645808233 Simplifying x + -5.5 = 8.645808233 Reorder the terms: -5.5 + x = 8.645808233 Solving -5.5 + x = 8.645808233 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 = 8.645808233 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 8.645808233 + 5.5 x = 8.645808233 + 5.5 Combine like terms: 8.645808233 + 5.5 = 14.145808233 x = 14.145808233 Simplifying x = 14.145808233Subproblem 2
x + -5.5 = -8.645808233 Simplifying x + -5.5 = -8.645808233 Reorder the terms: -5.5 + x = -8.645808233 Solving -5.5 + x = -8.645808233 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 = -8.645808233 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -8.645808233 + 5.5 x = -8.645808233 + 5.5 Combine like terms: -8.645808233 + 5.5 = -3.145808233 x = -3.145808233 Simplifying x = -3.145808233Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.145808233, -3.145808233}
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