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Simplifying 24x2 + 34x + 5 = 4 Reorder the terms: 5 + 34x + 24x2 = 4 Solving 5 + 34x + 24x2 = 4 Solving for variable 'x'. Reorder the terms: 5 + -4 + 34x + 24x2 = 4 + -4 Combine like terms: 5 + -4 = 1 1 + 34x + 24x2 = 4 + -4 Combine like terms: 4 + -4 = 0 1 + 34x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.04166666667 + 1.416666667x + x2 = 0 Move the constant term to the right: Add '-0.04166666667' to each side of the equation. 0.04166666667 + 1.416666667x + -0.04166666667 + x2 = 0 + -0.04166666667 Reorder the terms: 0.04166666667 + -0.04166666667 + 1.416666667x + x2 = 0 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + 1.416666667x + x2 = 0 + -0.04166666667 1.416666667x + x2 = 0 + -0.04166666667 Combine like terms: 0 + -0.04166666667 = -0.04166666667 1.416666667x + x2 = -0.04166666667 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 = -0.04166666667 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667x + x2 = -0.04166666667 + 0.5017361113 Combine like terms: -0.04166666667 + 0.5017361113 = 0.46006944463 0.5017361113 + 1.416666667x + x2 = 0.46006944463 Factor a perfect square on the left side: (x + 0.7083333335)(x + 0.7083333335) = 0.46006944463 Calculate the square root of the right side: 0.678284192 Break this problem into two subproblems by setting (x + 0.7083333335) equal to 0.678284192 and -0.678284192.Subproblem 1
x + 0.7083333335 = 0.678284192 Simplifying x + 0.7083333335 = 0.678284192 Reorder the terms: 0.7083333335 + x = 0.678284192 Solving 0.7083333335 + x = 0.678284192 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 = 0.678284192 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 0.678284192 + -0.7083333335 x = 0.678284192 + -0.7083333335 Combine like terms: 0.678284192 + -0.7083333335 = -0.0300491415 x = -0.0300491415 Simplifying x = -0.0300491415Subproblem 2
x + 0.7083333335 = -0.678284192 Simplifying x + 0.7083333335 = -0.678284192 Reorder the terms: 0.7083333335 + x = -0.678284192 Solving 0.7083333335 + x = -0.678284192 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 = -0.678284192 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -0.678284192 + -0.7083333335 x = -0.678284192 + -0.7083333335 Combine like terms: -0.678284192 + -0.7083333335 = -1.3866175255 x = -1.3866175255 Simplifying x = -1.3866175255Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0300491415, -1.3866175255}
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