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Simplifying 2x(8x + -5) = (5 + -4x) Reorder the terms: 2x(-5 + 8x) = (5 + -4x) (-5 * 2x + 8x * 2x) = (5 + -4x) (-10x + 16x2) = (5 + -4x) Remove parenthesis around (5 + -4x) -10x + 16x2 = 5 + -4x Solving -10x + 16x2 = 5 + -4x Solving for variable 'x'. Reorder the terms: -5 + -10x + 4x + 16x2 = 5 + -4x + -5 + 4x Combine like terms: -10x + 4x = -6x -5 + -6x + 16x2 = 5 + -4x + -5 + 4x Reorder the terms: -5 + -6x + 16x2 = 5 + -5 + -4x + 4x Combine like terms: 5 + -5 = 0 -5 + -6x + 16x2 = 0 + -4x + 4x -5 + -6x + 16x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -5 + -6x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -0.375x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -0.375x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -0.375x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -0.375x + x2 = 0 + 0.3125 -0.375x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -0.375x + x2 = 0.3125 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 0.3125 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 0.3125 + 0.03515625 Combine like terms: 0.3125 + 0.03515625 = 0.34765625 0.03515625 + -0.375x + x2 = 0.34765625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.34765625 Calculate the square root of the right side: 0.589623821 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.589623821 and -0.589623821.Subproblem 1
x + -0.1875 = 0.589623821 Simplifying x + -0.1875 = 0.589623821 Reorder the terms: -0.1875 + x = 0.589623821 Solving -0.1875 + x = 0.589623821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.589623821 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.589623821 + 0.1875 x = 0.589623821 + 0.1875 Combine like terms: 0.589623821 + 0.1875 = 0.777123821 x = 0.777123821 Simplifying x = 0.777123821Subproblem 2
x + -0.1875 = -0.589623821 Simplifying x + -0.1875 = -0.589623821 Reorder the terms: -0.1875 + x = -0.589623821 Solving -0.1875 + x = -0.589623821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.589623821 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.589623821 + 0.1875 x = -0.589623821 + 0.1875 Combine like terms: -0.589623821 + 0.1875 = -0.402123821 x = -0.402123821 Simplifying x = -0.402123821Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.777123821, -0.402123821}
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