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Simplifying -26x2 + 88x + -29 = 0 Reorder the terms: -29 + 88x + -26x2 = 0 Solving -29 + 88x + -26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -26 the coefficient of the squared term: Divide each side by '-26'. 1.115384615 + -3.384615385x + x2 = 0 Move the constant term to the right: Add '-1.115384615' to each side of the equation. 1.115384615 + -3.384615385x + -1.115384615 + x2 = 0 + -1.115384615 Reorder the terms: 1.115384615 + -1.115384615 + -3.384615385x + x2 = 0 + -1.115384615 Combine like terms: 1.115384615 + -1.115384615 = 0.000000000 0.000000000 + -3.384615385x + x2 = 0 + -1.115384615 -3.384615385x + x2 = 0 + -1.115384615 Combine like terms: 0 + -1.115384615 = -1.115384615 -3.384615385x + x2 = -1.115384615 The x term is -3.384615385x. Take half its coefficient (-1.692307693). Square it (2.863905328) and add it to both sides. Add '2.863905328' to each side of the equation. -3.384615385x + 2.863905328 + x2 = -1.115384615 + 2.863905328 Reorder the terms: 2.863905328 + -3.384615385x + x2 = -1.115384615 + 2.863905328 Combine like terms: -1.115384615 + 2.863905328 = 1.748520713 2.863905328 + -3.384615385x + x2 = 1.748520713 Factor a perfect square on the left side: (x + -1.692307693)(x + -1.692307693) = 1.748520713 Calculate the square root of the right side: 1.322316419 Break this problem into two subproblems by setting (x + -1.692307693) equal to 1.322316419 and -1.322316419.Subproblem 1
x + -1.692307693 = 1.322316419 Simplifying x + -1.692307693 = 1.322316419 Reorder the terms: -1.692307693 + x = 1.322316419 Solving -1.692307693 + x = 1.322316419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.692307693' to each side of the equation. -1.692307693 + 1.692307693 + x = 1.322316419 + 1.692307693 Combine like terms: -1.692307693 + 1.692307693 = 0.000000000 0.000000000 + x = 1.322316419 + 1.692307693 x = 1.322316419 + 1.692307693 Combine like terms: 1.322316419 + 1.692307693 = 3.014624112 x = 3.014624112 Simplifying x = 3.014624112Subproblem 2
x + -1.692307693 = -1.322316419 Simplifying x + -1.692307693 = -1.322316419 Reorder the terms: -1.692307693 + x = -1.322316419 Solving -1.692307693 + x = -1.322316419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.692307693' to each side of the equation. -1.692307693 + 1.692307693 + x = -1.322316419 + 1.692307693 Combine like terms: -1.692307693 + 1.692307693 = 0.000000000 0.000000000 + x = -1.322316419 + 1.692307693 x = -1.322316419 + 1.692307693 Combine like terms: -1.322316419 + 1.692307693 = 0.369991274 x = 0.369991274 Simplifying x = 0.369991274Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.014624112, 0.369991274}
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