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Simplifying 24x2 + 34x + -15 = 0 Reorder the terms: -15 + 34x + 24x2 = 0 Solving -15 + 34x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.625 + 1.416666667x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 1.416666667x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 1.416666667x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 1.416666667x + x2 = 0 + 0.625 1.416666667x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 1.416666667x + x2 = 0.625 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 = 0.625 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667x + x2 = 0.625 + 0.5017361113 Combine like terms: 0.625 + 0.5017361113 = 1.1267361113 0.5017361113 + 1.416666667x + x2 = 1.1267361113 Factor a perfect square on the left side: (x + 0.7083333335)(x + 0.7083333335) = 1.1267361113 Calculate the square root of the right side: 1.061478267 Break this problem into two subproblems by setting (x + 0.7083333335) equal to 1.061478267 and -1.061478267.Subproblem 1
x + 0.7083333335 = 1.061478267 Simplifying x + 0.7083333335 = 1.061478267 Reorder the terms: 0.7083333335 + x = 1.061478267 Solving 0.7083333335 + x = 1.061478267 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 = 1.061478267 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 1.061478267 + -0.7083333335 x = 1.061478267 + -0.7083333335 Combine like terms: 1.061478267 + -0.7083333335 = 0.3531449335 x = 0.3531449335 Simplifying x = 0.3531449335Subproblem 2
x + 0.7083333335 = -1.061478267 Simplifying x + 0.7083333335 = -1.061478267 Reorder the terms: 0.7083333335 + x = -1.061478267 Solving 0.7083333335 + x = -1.061478267 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 = -1.061478267 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -1.061478267 + -0.7083333335 x = -1.061478267 + -0.7083333335 Combine like terms: -1.061478267 + -0.7083333335 = -1.7698116005 x = -1.7698116005 Simplifying x = -1.7698116005Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3531449335, -1.7698116005}
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