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Simplifying (5x + -2)(5x + -2) = 27 Reorder the terms: (-2 + 5x)(5x + -2) = 27 Reorder the terms: (-2 + 5x)(-2 + 5x) = 27 Multiply (-2 + 5x) * (-2 + 5x) (-2(-2 + 5x) + 5x * (-2 + 5x)) = 27 ((-2 * -2 + 5x * -2) + 5x * (-2 + 5x)) = 27 ((4 + -10x) + 5x * (-2 + 5x)) = 27 (4 + -10x + (-2 * 5x + 5x * 5x)) = 27 (4 + -10x + (-10x + 25x2)) = 27 Combine like terms: -10x + -10x = -20x (4 + -20x + 25x2) = 27 Solving 4 + -20x + 25x2 = 27 Solving for variable 'x'. Reorder the terms: 4 + -27 + -20x + 25x2 = 27 + -27 Combine like terms: 4 + -27 = -23 -23 + -20x + 25x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -23 + -20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.92 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.92' to each side of the equation. -0.92 + -0.8x + 0.92 + x2 = 0 + 0.92 Reorder the terms: -0.92 + 0.92 + -0.8x + x2 = 0 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + -0.8x + x2 = 0 + 0.92 -0.8x + x2 = 0 + 0.92 Combine like terms: 0 + 0.92 = 0.92 -0.8x + x2 = 0.92 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.92 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.92 + 0.16 Combine like terms: 0.92 + 0.16 = 1.08 0.16 + -0.8x + x2 = 1.08 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 1.08 Calculate the square root of the right side: 1.039230485 Break this problem into two subproblems by setting (x + -0.4) equal to 1.039230485 and -1.039230485.Subproblem 1
x + -0.4 = 1.039230485 Simplifying x + -0.4 = 1.039230485 Reorder the terms: -0.4 + x = 1.039230485 Solving -0.4 + x = 1.039230485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.039230485 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.039230485 + 0.4 x = 1.039230485 + 0.4 Combine like terms: 1.039230485 + 0.4 = 1.439230485 x = 1.439230485 Simplifying x = 1.439230485Subproblem 2
x + -0.4 = -1.039230485 Simplifying x + -0.4 = -1.039230485 Reorder the terms: -0.4 + x = -1.039230485 Solving -0.4 + x = -1.039230485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.039230485 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.039230485 + 0.4 x = -1.039230485 + 0.4 Combine like terms: -1.039230485 + 0.4 = -0.639230485 x = -0.639230485 Simplifying x = -0.639230485Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.439230485, -0.639230485}
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