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Simplifying 12x2 + 26x + -45 = 0 Reorder the terms: -45 + 26x + 12x2 = 0 Solving -45 + 26x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.75 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 2.166666667x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 2.166666667x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 2.166666667x + x2 = 0 + 3.75 2.166666667x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 2.166666667x + x2 = 3.75 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 = 3.75 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 3.75 + 1.173611113 Combine like terms: 3.75 + 1.173611113 = 4.923611113 1.173611113 + 2.166666667x + x2 = 4.923611113 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 4.923611113 Calculate the square root of the right side: 2.21892116 Break this problem into two subproblems by setting (x + 1.083333334) equal to 2.21892116 and -2.21892116.Subproblem 1
x + 1.083333334 = 2.21892116 Simplifying x + 1.083333334 = 2.21892116 Reorder the terms: 1.083333334 + x = 2.21892116 Solving 1.083333334 + x = 2.21892116 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 = 2.21892116 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 2.21892116 + -1.083333334 x = 2.21892116 + -1.083333334 Combine like terms: 2.21892116 + -1.083333334 = 1.135587826 x = 1.135587826 Simplifying x = 1.135587826Subproblem 2
x + 1.083333334 = -2.21892116 Simplifying x + 1.083333334 = -2.21892116 Reorder the terms: 1.083333334 + x = -2.21892116 Solving 1.083333334 + x = -2.21892116 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 = -2.21892116 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -2.21892116 + -1.083333334 x = -2.21892116 + -1.083333334 Combine like terms: -2.21892116 + -1.083333334 = -3.302254494 x = -3.302254494 Simplifying x = -3.302254494Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.135587826, -3.302254494}
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