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Simplifying 2x2 + 5x + -0.66 = 0 Reorder the terms: -0.66 + 5x + 2x2 = 0 Solving -0.66 + 5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.33 + 2.5x + x2 = 0 Move the constant term to the right: Add '0.33' to each side of the equation. -0.33 + 2.5x + 0.33 + x2 = 0 + 0.33 Reorder the terms: -0.33 + 0.33 + 2.5x + x2 = 0 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + 2.5x + x2 = 0 + 0.33 2.5x + x2 = 0 + 0.33 Combine like terms: 0 + 0.33 = 0.33 2.5x + x2 = 0.33 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 0.33 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.33 + 1.5625 Combine like terms: 0.33 + 1.5625 = 1.8925 1.5625 + 2.5x + x2 = 1.8925 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.8925 Calculate the square root of the right side: 1.375681649 Break this problem into two subproblems by setting (x + 1.25) equal to 1.375681649 and -1.375681649.Subproblem 1
x + 1.25 = 1.375681649 Simplifying x + 1.25 = 1.375681649 Reorder the terms: 1.25 + x = 1.375681649 Solving 1.25 + x = 1.375681649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.375681649 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.375681649 + -1.25 x = 1.375681649 + -1.25 Combine like terms: 1.375681649 + -1.25 = 0.125681649 x = 0.125681649 Simplifying x = 0.125681649Subproblem 2
x + 1.25 = -1.375681649 Simplifying x + 1.25 = -1.375681649 Reorder the terms: 1.25 + x = -1.375681649 Solving 1.25 + x = -1.375681649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.375681649 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.375681649 + -1.25 x = -1.375681649 + -1.25 Combine like terms: -1.375681649 + -1.25 = -2.625681649 x = -2.625681649 Simplifying x = -2.625681649Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.125681649, -2.625681649}
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