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Simplifying 5(2x + -1) * x + 17 = 5x + 6(x + 2) Reorder the terms: 5(-1 + 2x) * x + 17 = 5x + 6(x + 2) Reorder the terms for easier multiplication: 5x(-1 + 2x) + 17 = 5x + 6(x + 2) (-1 * 5x + 2x * 5x) + 17 = 5x + 6(x + 2) (-5x + 10x2) + 17 = 5x + 6(x + 2) Reorder the terms: 17 + -5x + 10x2 = 5x + 6(x + 2) Reorder the terms: 17 + -5x + 10x2 = 5x + 6(2 + x) 17 + -5x + 10x2 = 5x + (2 * 6 + x * 6) 17 + -5x + 10x2 = 5x + (12 + 6x) Reorder the terms: 17 + -5x + 10x2 = 12 + 5x + 6x Combine like terms: 5x + 6x = 11x 17 + -5x + 10x2 = 12 + 11x Solving 17 + -5x + 10x2 = 12 + 11x Solving for variable 'x'. Reorder the terms: 17 + -12 + -5x + -11x + 10x2 = 12 + 11x + -12 + -11x Combine like terms: 17 + -12 = 5 5 + -5x + -11x + 10x2 = 12 + 11x + -12 + -11x Combine like terms: -5x + -11x = -16x 5 + -16x + 10x2 = 12 + 11x + -12 + -11x Reorder the terms: 5 + -16x + 10x2 = 12 + -12 + 11x + -11x Combine like terms: 12 + -12 = 0 5 + -16x + 10x2 = 0 + 11x + -11x 5 + -16x + 10x2 = 11x + -11x Combine like terms: 11x + -11x = 0 5 + -16x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.5 + -1.6x + x2 = 0.0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.6x + -0.5 + x2 = 0.0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.6x + x2 = 0.0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.6x + x2 = 0.0 + -0.5 -1.6x + x2 = 0.0 + -0.5 Combine like terms: 0.0 + -0.5 = -0.5 -1.6x + x2 = -0.5 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = -0.5 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -0.5 + 0.64 Combine like terms: -0.5 + 0.64 = 0.14 0.64 + -1.6x + x2 = 0.14 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.14 Calculate the square root of the right side: 0.374165739 Break this problem into two subproblems by setting (x + -0.8) equal to 0.374165739 and -0.374165739.Subproblem 1
x + -0.8 = 0.374165739 Simplifying x + -0.8 = 0.374165739 Reorder the terms: -0.8 + x = 0.374165739 Solving -0.8 + x = 0.374165739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0.374165739 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.374165739 + 0.8 x = 0.374165739 + 0.8 Combine like terms: 0.374165739 + 0.8 = 1.174165739 x = 1.174165739 Simplifying x = 1.174165739Subproblem 2
x + -0.8 = -0.374165739 Simplifying x + -0.8 = -0.374165739 Reorder the terms: -0.8 + x = -0.374165739 Solving -0.8 + x = -0.374165739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -0.374165739 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -0.374165739 + 0.8 x = -0.374165739 + 0.8 Combine like terms: -0.374165739 + 0.8 = 0.425834261 x = 0.425834261 Simplifying x = 0.425834261Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.174165739, 0.425834261}
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