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Simplifying -5x(1 + -5x) + (-8x + -2) = -4x + -8x (1 * -5x + -5x * -5x) + (-8x + -2) = -4x + -8x (-5x + 25x2) + (-8x + -2) = -4x + -8x Reorder the terms: -5x + 25x2 + (-2 + -8x) = -4x + -8x Remove parenthesis around (-2 + -8x) -5x + 25x2 + -2 + -8x = -4x + -8x Reorder the terms: -2 + -5x + -8x + 25x2 = -4x + -8x Combine like terms: -5x + -8x = -13x -2 + -13x + 25x2 = -4x + -8x Combine like terms: -4x + -8x = -12x -2 + -13x + 25x2 = -12x Solving -2 + -13x + 25x2 = -12x Solving for variable 'x'. Reorder the terms: -2 + -13x + 12x + 25x2 = -12x + 12x Combine like terms: -13x + 12x = -1x -2 + -1x + 25x2 = -12x + 12x Combine like terms: -12x + 12x = 0 -2 + -1x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.08 + -0.04x + x2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + -0.04x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + -0.04x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + -0.04x + x2 = 0 + 0.08 -0.04x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 -0.04x + x2 = 0.08 The x term is -0.04x. Take half its coefficient (-0.02). Square it (0.0004) and add it to both sides. Add '0.0004' to each side of the equation. -0.04x + 0.0004 + x2 = 0.08 + 0.0004 Reorder the terms: 0.0004 + -0.04x + x2 = 0.08 + 0.0004 Combine like terms: 0.08 + 0.0004 = 0.0804 0.0004 + -0.04x + x2 = 0.0804 Factor a perfect square on the left side: (x + -0.02)(x + -0.02) = 0.0804 Calculate the square root of the right side: 0.283548938 Break this problem into two subproblems by setting (x + -0.02) equal to 0.283548938 and -0.283548938.Subproblem 1
x + -0.02 = 0.283548938 Simplifying x + -0.02 = 0.283548938 Reorder the terms: -0.02 + x = 0.283548938 Solving -0.02 + x = 0.283548938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = 0.283548938 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = 0.283548938 + 0.02 x = 0.283548938 + 0.02 Combine like terms: 0.283548938 + 0.02 = 0.303548938 x = 0.303548938 Simplifying x = 0.303548938Subproblem 2
x + -0.02 = -0.283548938 Simplifying x + -0.02 = -0.283548938 Reorder the terms: -0.02 + x = -0.283548938 Solving -0.02 + x = -0.283548938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = -0.283548938 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = -0.283548938 + 0.02 x = -0.283548938 + 0.02 Combine like terms: -0.283548938 + 0.02 = -0.263548938 x = -0.263548938 Simplifying x = -0.263548938Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.303548938, -0.263548938}
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