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Simplifying 24x2 + -34x = 5 Reorder the terms: -34x + 24x2 = 5 Solving -34x + 24x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -34x + 24x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -34x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.2083333333 + -1.416666667x + x2 = 0 Move the constant term to the right: Add '0.2083333333' to each side of the equation. -0.2083333333 + -1.416666667x + 0.2083333333 + x2 = 0 + 0.2083333333 Reorder the terms: -0.2083333333 + 0.2083333333 + -1.416666667x + x2 = 0 + 0.2083333333 Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000 0.0000000000 + -1.416666667x + x2 = 0 + 0.2083333333 -1.416666667x + x2 = 0 + 0.2083333333 Combine like terms: 0 + 0.2083333333 = 0.2083333333 -1.416666667x + x2 = 0.2083333333 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 = 0.2083333333 + 0.5017361113 Reorder the terms: 0.5017361113 + -1.416666667x + x2 = 0.2083333333 + 0.5017361113 Combine like terms: 0.2083333333 + 0.5017361113 = 0.7100694446 0.5017361113 + -1.416666667x + x2 = 0.7100694446 Factor a perfect square on the left side: (x + -0.7083333335)(x + -0.7083333335) = 0.7100694446 Calculate the square root of the right side: 0.842656184 Break this problem into two subproblems by setting (x + -0.7083333335) equal to 0.842656184 and -0.842656184.Subproblem 1
x + -0.7083333335 = 0.842656184 Simplifying x + -0.7083333335 = 0.842656184 Reorder the terms: -0.7083333335 + x = 0.842656184 Solving -0.7083333335 + x = 0.842656184 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 = 0.842656184 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = 0.842656184 + 0.7083333335 x = 0.842656184 + 0.7083333335 Combine like terms: 0.842656184 + 0.7083333335 = 1.5509895175 x = 1.5509895175 Simplifying x = 1.5509895175Subproblem 2
x + -0.7083333335 = -0.842656184 Simplifying x + -0.7083333335 = -0.842656184 Reorder the terms: -0.7083333335 + x = -0.842656184 Solving -0.7083333335 + x = -0.842656184 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 = -0.842656184 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = -0.842656184 + 0.7083333335 x = -0.842656184 + 0.7083333335 Combine like terms: -0.842656184 + 0.7083333335 = -0.1343228505 x = -0.1343228505 Simplifying x = -0.1343228505Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5509895175, -0.1343228505}
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