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Simplifying 0.285x2 + -2x + 2 = 0 Reorder the terms: 2 + -2x + 0.285x2 = 0 Solving 2 + -2x + 0.285x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.285 the coefficient of the squared term: Divide each side by '0.285'. 7.01754386 + -7.01754386x + x2 = 0 Move the constant term to the right: Add '-7.01754386' to each side of the equation. 7.01754386 + -7.01754386x + -7.01754386 + x2 = 0 + -7.01754386 Reorder the terms: 7.01754386 + -7.01754386 + -7.01754386x + x2 = 0 + -7.01754386 Combine like terms: 7.01754386 + -7.01754386 = 0.00000000 0.00000000 + -7.01754386x + x2 = 0 + -7.01754386 -7.01754386x + x2 = 0 + -7.01754386 Combine like terms: 0 + -7.01754386 = -7.01754386 -7.01754386x + x2 = -7.01754386 The x term is -7.01754386x. Take half its coefficient (-3.50877193). Square it (12.31148046) and add it to both sides. Add '12.31148046' to each side of the equation. -7.01754386x + 12.31148046 + x2 = -7.01754386 + 12.31148046 Reorder the terms: 12.31148046 + -7.01754386x + x2 = -7.01754386 + 12.31148046 Combine like terms: -7.01754386 + 12.31148046 = 5.2939366 12.31148046 + -7.01754386x + x2 = 5.2939366 Factor a perfect square on the left side: (x + -3.50877193)(x + -3.50877193) = 5.2939366 Calculate the square root of the right side: 2.300855623 Break this problem into two subproblems by setting (x + -3.50877193) equal to 2.300855623 and -2.300855623.Subproblem 1
x + -3.50877193 = 2.300855623 Simplifying x + -3.50877193 = 2.300855623 Reorder the terms: -3.50877193 + x = 2.300855623 Solving -3.50877193 + x = 2.300855623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.50877193' to each side of the equation. -3.50877193 + 3.50877193 + x = 2.300855623 + 3.50877193 Combine like terms: -3.50877193 + 3.50877193 = 0.00000000 0.00000000 + x = 2.300855623 + 3.50877193 x = 2.300855623 + 3.50877193 Combine like terms: 2.300855623 + 3.50877193 = 5.809627553 x = 5.809627553 Simplifying x = 5.809627553Subproblem 2
x + -3.50877193 = -2.300855623 Simplifying x + -3.50877193 = -2.300855623 Reorder the terms: -3.50877193 + x = -2.300855623 Solving -3.50877193 + x = -2.300855623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.50877193' to each side of the equation. -3.50877193 + 3.50877193 + x = -2.300855623 + 3.50877193 Combine like terms: -3.50877193 + 3.50877193 = 0.00000000 0.00000000 + x = -2.300855623 + 3.50877193 x = -2.300855623 + 3.50877193 Combine like terms: -2.300855623 + 3.50877193 = 1.207916307 x = 1.207916307 Simplifying x = 1.207916307Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.809627553, 1.207916307}
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