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Simplifying 17x(5x + -6) = 48 Reorder the terms: 17x(-6 + 5x) = 48 (-6 * 17x + 5x * 17x) = 48 (-102x + 85x2) = 48 Solving -102x + 85x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + -102x + 85x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -102x + 85x2 = 0 Begin completing the square. Divide all terms by 85 the coefficient of the squared term: Divide each side by '85'. -0.5647058824 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.5647058824' to each side of the equation. -0.5647058824 + -1.2x + 0.5647058824 + x2 = 0 + 0.5647058824 Reorder the terms: -0.5647058824 + 0.5647058824 + -1.2x + x2 = 0 + 0.5647058824 Combine like terms: -0.5647058824 + 0.5647058824 = 0.0000000000 0.0000000000 + -1.2x + x2 = 0 + 0.5647058824 -1.2x + x2 = 0 + 0.5647058824 Combine like terms: 0 + 0.5647058824 = 0.5647058824 -1.2x + x2 = 0.5647058824 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.5647058824 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.5647058824 + 0.36 Combine like terms: 0.5647058824 + 0.36 = 0.9247058824 0.36 + -1.2x + x2 = 0.9247058824 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.9247058824 Calculate the square root of the right side: 0.961616286 Break this problem into two subproblems by setting (x + -0.6) equal to 0.961616286 and -0.961616286.Subproblem 1
x + -0.6 = 0.961616286 Simplifying x + -0.6 = 0.961616286 Reorder the terms: -0.6 + x = 0.961616286 Solving -0.6 + x = 0.961616286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.961616286 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.961616286 + 0.6 x = 0.961616286 + 0.6 Combine like terms: 0.961616286 + 0.6 = 1.561616286 x = 1.561616286 Simplifying x = 1.561616286Subproblem 2
x + -0.6 = -0.961616286 Simplifying x + -0.6 = -0.961616286 Reorder the terms: -0.6 + x = -0.961616286 Solving -0.6 + x = -0.961616286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.961616286 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.961616286 + 0.6 x = -0.961616286 + 0.6 Combine like terms: -0.961616286 + 0.6 = -0.361616286 x = -0.361616286 Simplifying x = -0.361616286Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.561616286, -0.361616286}
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