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Simplifying 10x2 + x + -10 = 2x + 8 Reorder the terms: -10 + x + 10x2 = 2x + 8 Reorder the terms: -10 + x + 10x2 = 8 + 2x Solving -10 + x + 10x2 = 8 + 2x Solving for variable 'x'. Reorder the terms: -10 + -8 + x + -2x + 10x2 = 8 + 2x + -8 + -2x Combine like terms: -10 + -8 = -18 -18 + x + -2x + 10x2 = 8 + 2x + -8 + -2x Combine like terms: x + -2x = -1x -18 + -1x + 10x2 = 8 + 2x + -8 + -2x Reorder the terms: -18 + -1x + 10x2 = 8 + -8 + 2x + -2x Combine like terms: 8 + -8 = 0 -18 + -1x + 10x2 = 0 + 2x + -2x -18 + -1x + 10x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -18 + -1x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.8 + -0.1x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -0.1x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -0.1x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -0.1x + x2 = 0 + 1.8 -0.1x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -0.1x + x2 = 1.8 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 1.8 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 1.8 + 0.0025 Combine like terms: 1.8 + 0.0025 = 1.8025 0.0025 + -0.1x + x2 = 1.8025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 1.8025 Calculate the square root of the right side: 1.342572158 Break this problem into two subproblems by setting (x + -0.05) equal to 1.342572158 and -1.342572158.Subproblem 1
x + -0.05 = 1.342572158 Simplifying x + -0.05 = 1.342572158 Reorder the terms: -0.05 + x = 1.342572158 Solving -0.05 + x = 1.342572158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 1.342572158 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 1.342572158 + 0.05 x = 1.342572158 + 0.05 Combine like terms: 1.342572158 + 0.05 = 1.392572158 x = 1.392572158 Simplifying x = 1.392572158Subproblem 2
x + -0.05 = -1.342572158 Simplifying x + -0.05 = -1.342572158 Reorder the terms: -0.05 + x = -1.342572158 Solving -0.05 + x = -1.342572158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -1.342572158 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -1.342572158 + 0.05 x = -1.342572158 + 0.05 Combine like terms: -1.342572158 + 0.05 = -1.292572158 x = -1.292572158 Simplifying x = -1.292572158Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.392572158, -1.292572158}
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