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Simplifying 10x2 + 11x + -2 = 0 Reorder the terms: -2 + 11x + 10x2 = 0 Solving -2 + 11x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + 1.1x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 1.1x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 1.1x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 1.1x + x2 = 0 + 0.2 1.1x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 1.1x + x2 = 0.2 The x term is 1.1x. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1x + 0.3025 + x2 = 0.2 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 0.2 + 0.3025 Combine like terms: 0.2 + 0.3025 = 0.5025 0.3025 + 1.1x + x2 = 0.5025 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 0.5025 Calculate the square root of the right side: 0.708872344 Break this problem into two subproblems by setting (x + 0.55) equal to 0.708872344 and -0.708872344.Subproblem 1
x + 0.55 = 0.708872344 Simplifying x + 0.55 = 0.708872344 Reorder the terms: 0.55 + x = 0.708872344 Solving 0.55 + x = 0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = 0.708872344 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 0.708872344 + -0.55 x = 0.708872344 + -0.55 Combine like terms: 0.708872344 + -0.55 = 0.158872344 x = 0.158872344 Simplifying x = 0.158872344Subproblem 2
x + 0.55 = -0.708872344 Simplifying x + 0.55 = -0.708872344 Reorder the terms: 0.55 + x = -0.708872344 Solving 0.55 + x = -0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = -0.708872344 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -0.708872344 + -0.55 x = -0.708872344 + -0.55 Combine like terms: -0.708872344 + -0.55 = -1.258872344 x = -1.258872344 Simplifying x = -1.258872344Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.158872344, -1.258872344}
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