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Simplifying 2x(8x + -7) = -5(-5x + 1) Reorder the terms: 2x(-7 + 8x) = -5(-5x + 1) (-7 * 2x + 8x * 2x) = -5(-5x + 1) (-14x + 16x2) = -5(-5x + 1) Reorder the terms: -14x + 16x2 = -5(1 + -5x) -14x + 16x2 = (1 * -5 + -5x * -5) -14x + 16x2 = (-5 + 25x) Solving -14x + 16x2 = -5 + 25x Solving for variable 'x'. Reorder the terms: 5 + -14x + -25x + 16x2 = -5 + 25x + 5 + -25x Combine like terms: -14x + -25x = -39x 5 + -39x + 16x2 = -5 + 25x + 5 + -25x Reorder the terms: 5 + -39x + 16x2 = -5 + 5 + 25x + -25x Combine like terms: -5 + 5 = 0 5 + -39x + 16x2 = 0 + 25x + -25x 5 + -39x + 16x2 = 25x + -25x Combine like terms: 25x + -25x = 0 5 + -39x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + -2.4375x + x2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -2.4375x + -0.3125 + x2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -2.4375x + x2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -2.4375x + x2 = 0 + -0.3125 -2.4375x + x2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -2.4375x + x2 = -0.3125 The x term is -2.4375x. Take half its coefficient (-1.21875). Square it (1.485351563) and add it to both sides. Add '1.485351563' to each side of the equation. -2.4375x + 1.485351563 + x2 = -0.3125 + 1.485351563 Reorder the terms: 1.485351563 + -2.4375x + x2 = -0.3125 + 1.485351563 Combine like terms: -0.3125 + 1.485351563 = 1.172851563 1.485351563 + -2.4375x + x2 = 1.172851563 Factor a perfect square on the left side: (x + -1.21875)(x + -1.21875) = 1.172851563 Calculate the square root of the right side: 1.082982716 Break this problem into two subproblems by setting (x + -1.21875) equal to 1.082982716 and -1.082982716.Subproblem 1
x + -1.21875 = 1.082982716 Simplifying x + -1.21875 = 1.082982716 Reorder the terms: -1.21875 + x = 1.082982716 Solving -1.21875 + x = 1.082982716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.21875' to each side of the equation. -1.21875 + 1.21875 + x = 1.082982716 + 1.21875 Combine like terms: -1.21875 + 1.21875 = 0.00000 0.00000 + x = 1.082982716 + 1.21875 x = 1.082982716 + 1.21875 Combine like terms: 1.082982716 + 1.21875 = 2.301732716 x = 2.301732716 Simplifying x = 2.301732716Subproblem 2
x + -1.21875 = -1.082982716 Simplifying x + -1.21875 = -1.082982716 Reorder the terms: -1.21875 + x = -1.082982716 Solving -1.21875 + x = -1.082982716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.21875' to each side of the equation. -1.21875 + 1.21875 + x = -1.082982716 + 1.21875 Combine like terms: -1.21875 + 1.21875 = 0.00000 0.00000 + x = -1.082982716 + 1.21875 x = -1.082982716 + 1.21875 Combine like terms: -1.082982716 + 1.21875 = 0.135767284 x = 0.135767284 Simplifying x = 0.135767284Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.301732716, 0.135767284}
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