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Simplifying 0 = -2x2 + 22x + -17 Reorder the terms: 0 = -17 + 22x + -2x2 Solving 0 = -17 + 22x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 17 = 17 17 + -22x + 2x2 = -17 + 22x + -2x2 + 17 + -22x + 2x2 Reorder the terms: 17 + -22x + 2x2 = -17 + 17 + 22x + -22x + -2x2 + 2x2 Combine like terms: -17 + 17 = 0 17 + -22x + 2x2 = 0 + 22x + -22x + -2x2 + 2x2 17 + -22x + 2x2 = 22x + -22x + -2x2 + 2x2 Combine like terms: 22x + -22x = 0 17 + -22x + 2x2 = 0 + -2x2 + 2x2 17 + -22x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 17 + -22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -11x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -11x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -11x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -11x + x2 = 0 + -8.5 -11x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -11x + x2 = -8.5 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 = -8.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -8.5 + 30.25 Combine like terms: -8.5 + 30.25 = 21.75 30.25 + -11x + x2 = 21.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 21.75 Calculate the square root of the right side: 4.663689527 Break this problem into two subproblems by setting (x + -5.5) equal to 4.663689527 and -4.663689527.Subproblem 1
x + -5.5 = 4.663689527 Simplifying x + -5.5 = 4.663689527 Reorder the terms: -5.5 + x = 4.663689527 Solving -5.5 + x = 4.663689527 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 = 4.663689527 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4.663689527 + 5.5 x = 4.663689527 + 5.5 Combine like terms: 4.663689527 + 5.5 = 10.163689527 x = 10.163689527 Simplifying x = 10.163689527Subproblem 2
x + -5.5 = -4.663689527 Simplifying x + -5.5 = -4.663689527 Reorder the terms: -5.5 + x = -4.663689527 Solving -5.5 + x = -4.663689527 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 = -4.663689527 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4.663689527 + 5.5 x = -4.663689527 + 5.5 Combine like terms: -4.663689527 + 5.5 = 0.836310473 x = 0.836310473 Simplifying x = 0.836310473Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.163689527, 0.836310473}
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