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Simplifying 13x2 = 18x + 27 Reorder the terms: 13x2 = 27 + 18x Solving 13x2 = 27 + 18x Solving for variable 'x'. Reorder the terms: -27 + -18x + 13x2 = 27 + 18x + -27 + -18x Reorder the terms: -27 + -18x + 13x2 = 27 + -27 + 18x + -18x Combine like terms: 27 + -27 = 0 -27 + -18x + 13x2 = 0 + 18x + -18x -27 + -18x + 13x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -27 + -18x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -2.076923077 + -1.384615385x + x2 = 0 Move the constant term to the right: Add '2.076923077' to each side of the equation. -2.076923077 + -1.384615385x + 2.076923077 + x2 = 0 + 2.076923077 Reorder the terms: -2.076923077 + 2.076923077 + -1.384615385x + x2 = 0 + 2.076923077 Combine like terms: -2.076923077 + 2.076923077 = 0.000000000 0.000000000 + -1.384615385x + x2 = 0 + 2.076923077 -1.384615385x + x2 = 0 + 2.076923077 Combine like terms: 0 + 2.076923077 = 2.076923077 -1.384615385x + x2 = 2.076923077 The x term is -1.384615385x. Take half its coefficient (-0.6923076925). Square it (0.4792899411) and add it to both sides. Add '0.4792899411' to each side of the equation. -1.384615385x + 0.4792899411 + x2 = 2.076923077 + 0.4792899411 Reorder the terms: 0.4792899411 + -1.384615385x + x2 = 2.076923077 + 0.4792899411 Combine like terms: 2.076923077 + 0.4792899411 = 2.5562130181 0.4792899411 + -1.384615385x + x2 = 2.5562130181 Factor a perfect square on the left side: (x + -0.6923076925)(x + -0.6923076925) = 2.5562130181 Calculate the square root of the right side: 1.59881613 Break this problem into two subproblems by setting (x + -0.6923076925) equal to 1.59881613 and -1.59881613.Subproblem 1
x + -0.6923076925 = 1.59881613 Simplifying x + -0.6923076925 = 1.59881613 Reorder the terms: -0.6923076925 + x = 1.59881613 Solving -0.6923076925 + x = 1.59881613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6923076925' to each side of the equation. -0.6923076925 + 0.6923076925 + x = 1.59881613 + 0.6923076925 Combine like terms: -0.6923076925 + 0.6923076925 = 0.0000000000 0.0000000000 + x = 1.59881613 + 0.6923076925 x = 1.59881613 + 0.6923076925 Combine like terms: 1.59881613 + 0.6923076925 = 2.2911238225 x = 2.2911238225 Simplifying x = 2.2911238225Subproblem 2
x + -0.6923076925 = -1.59881613 Simplifying x + -0.6923076925 = -1.59881613 Reorder the terms: -0.6923076925 + x = -1.59881613 Solving -0.6923076925 + x = -1.59881613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6923076925' to each side of the equation. -0.6923076925 + 0.6923076925 + x = -1.59881613 + 0.6923076925 Combine like terms: -0.6923076925 + 0.6923076925 = 0.0000000000 0.0000000000 + x = -1.59881613 + 0.6923076925 x = -1.59881613 + 0.6923076925 Combine like terms: -1.59881613 + 0.6923076925 = -0.9065084375 x = -0.9065084375 Simplifying x = -0.9065084375Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2911238225, -0.9065084375}
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