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Simplifying 12x2 + 17x = 15 Reorder the terms: 17x + 12x2 = 15 Solving 17x + 12x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 17x + 12x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 17x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.25 + 1.416666667x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.416666667x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.416666667x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.416666667x + x2 = 0 + 1.25 1.416666667x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.416666667x + x2 = 1.25 The x term is 1.416666667x. Take half its coefficient (0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. 1.416666667x + 0.5017361113 + x2 = 1.25 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667x + x2 = 1.25 + 0.5017361113 Combine like terms: 1.25 + 0.5017361113 = 1.7517361113 0.5017361113 + 1.416666667x + x2 = 1.7517361113 Factor a perfect square on the left side: (x + 0.7083333335)(x + 0.7083333335) = 1.7517361113 Calculate the square root of the right side: 1.323531681 Break this problem into two subproblems by setting (x + 0.7083333335) equal to 1.323531681 and -1.323531681.Subproblem 1
x + 0.7083333335 = 1.323531681 Simplifying x + 0.7083333335 = 1.323531681 Reorder the terms: 0.7083333335 + x = 1.323531681 Solving 0.7083333335 + x = 1.323531681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + x = 1.323531681 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 1.323531681 + -0.7083333335 x = 1.323531681 + -0.7083333335 Combine like terms: 1.323531681 + -0.7083333335 = 0.6151983475 x = 0.6151983475 Simplifying x = 0.6151983475Subproblem 2
x + 0.7083333335 = -1.323531681 Simplifying x + 0.7083333335 = -1.323531681 Reorder the terms: 0.7083333335 + x = -1.323531681 Solving 0.7083333335 + x = -1.323531681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + x = -1.323531681 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -1.323531681 + -0.7083333335 x = -1.323531681 + -0.7083333335 Combine like terms: -1.323531681 + -0.7083333335 = -2.0318650145 x = -2.0318650145 Simplifying x = -2.0318650145Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6151983475, -2.0318650145}
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