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Simplifying 36x2 + -9x + 25 = 69x Reorder the terms: 25 + -9x + 36x2 = 69x Solving 25 + -9x + 36x2 = 69x Solving for variable 'x'. Reorder the terms: 25 + -9x + -69x + 36x2 = 69x + -69x Combine like terms: -9x + -69x = -78x 25 + -78x + 36x2 = 69x + -69x Combine like terms: 69x + -69x = 0 25 + -78x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.6944444444 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '-0.6944444444' to each side of the equation. 0.6944444444 + -2.166666667x + -0.6944444444 + x2 = 0 + -0.6944444444 Reorder the terms: 0.6944444444 + -0.6944444444 + -2.166666667x + x2 = 0 + -0.6944444444 Combine like terms: 0.6944444444 + -0.6944444444 = 0.0000000000 0.0000000000 + -2.166666667x + x2 = 0 + -0.6944444444 -2.166666667x + x2 = 0 + -0.6944444444 Combine like terms: 0 + -0.6944444444 = -0.6944444444 -2.166666667x + x2 = -0.6944444444 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = -0.6944444444 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = -0.6944444444 + 1.173611113 Combine like terms: -0.6944444444 + 1.173611113 = 0.4791666686 1.173611113 + -2.166666667x + x2 = 0.4791666686 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 0.4791666686 Calculate the square root of the right side: 0.692218657 Break this problem into two subproblems by setting (x + -1.083333334) equal to 0.692218657 and -0.692218657.Subproblem 1
x + -1.083333334 = 0.692218657 Simplifying x + -1.083333334 = 0.692218657 Reorder the terms: -1.083333334 + x = 0.692218657 Solving -1.083333334 + x = 0.692218657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 0.692218657 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 0.692218657 + 1.083333334 x = 0.692218657 + 1.083333334 Combine like terms: 0.692218657 + 1.083333334 = 1.775551991 x = 1.775551991 Simplifying x = 1.775551991Subproblem 2
x + -1.083333334 = -0.692218657 Simplifying x + -1.083333334 = -0.692218657 Reorder the terms: -1.083333334 + x = -0.692218657 Solving -1.083333334 + x = -0.692218657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -0.692218657 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -0.692218657 + 1.083333334 x = -0.692218657 + 1.083333334 Combine like terms: -0.692218657 + 1.083333334 = 0.391114677 x = 0.391114677 Simplifying x = 0.391114677Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.775551991, 0.391114677}
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