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Simplifying (5x + -5) * x(10 + -2) + x = 3 + -1 Reorder the terms: (-5 + 5x) * x(10 + -2) + x = 3 + -1 Combine like terms: 10 + -2 = 8 (-5 + 5x) * x(8) + x = 3 + -1 Reorder the terms for easier multiplication: 8x(-5 + 5x) + x = 3 + -1 (-5 * 8x + 5x * 8x) + x = 3 + -1 (-40x + 40x2) + x = 3 + -1 Reorder the terms: -40x + x + 40x2 = 3 + -1 Combine like terms: -40x + x = -39x -39x + 40x2 = 3 + -1 Combine like terms: 3 + -1 = 2 -39x + 40x2 = 2 Solving -39x + 40x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -39x + 40x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -39x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.05 + -0.975x + x2 = 0.0 Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + -0.975x + 0.05 + x2 = 0.0 + 0.05 Reorder the terms: -0.05 + 0.05 + -0.975x + x2 = 0.0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + -0.975x + x2 = 0.0 + 0.05 -0.975x + x2 = 0.0 + 0.05 Combine like terms: 0.0 + 0.05 = 0.05 -0.975x + x2 = 0.05 The x term is -0.975x. Take half its coefficient (-0.4875). Square it (0.23765625) and add it to both sides. Add '0.23765625' to each side of the equation. -0.975x + 0.23765625 + x2 = 0.05 + 0.23765625 Reorder the terms: 0.23765625 + -0.975x + x2 = 0.05 + 0.23765625 Combine like terms: 0.05 + 0.23765625 = 0.28765625 0.23765625 + -0.975x + x2 = 0.28765625 Factor a perfect square on the left side: (x + -0.4875)(x + -0.4875) = 0.28765625 Calculate the square root of the right side: 0.536335949 Break this problem into two subproblems by setting (x + -0.4875) equal to 0.536335949 and -0.536335949.Subproblem 1
x + -0.4875 = 0.536335949 Simplifying x + -0.4875 = 0.536335949 Reorder the terms: -0.4875 + x = 0.536335949 Solving -0.4875 + x = 0.536335949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4875' to each side of the equation. -0.4875 + 0.4875 + x = 0.536335949 + 0.4875 Combine like terms: -0.4875 + 0.4875 = 0.0000 0.0000 + x = 0.536335949 + 0.4875 x = 0.536335949 + 0.4875 Combine like terms: 0.536335949 + 0.4875 = 1.023835949 x = 1.023835949 Simplifying x = 1.023835949Subproblem 2
x + -0.4875 = -0.536335949 Simplifying x + -0.4875 = -0.536335949 Reorder the terms: -0.4875 + x = -0.536335949 Solving -0.4875 + x = -0.536335949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4875' to each side of the equation. -0.4875 + 0.4875 + x = -0.536335949 + 0.4875 Combine like terms: -0.4875 + 0.4875 = 0.0000 0.0000 + x = -0.536335949 + 0.4875 x = -0.536335949 + 0.4875 Combine like terms: -0.536335949 + 0.4875 = -0.048835949 x = -0.048835949 Simplifying x = -0.048835949Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.023835949, -0.048835949}
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