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Simplifying -0.8x2 + -1x + 3 = 0 Reorder the terms: 3 + -1x + -0.8x2 = 0 Solving 3 + -1x + -0.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. -3.75 + 1.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 1.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 1.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 1.25x + x2 = 0 + 3.75 1.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 1.25x + x2 = 3.75 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 3.75 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 3.75 + 0.390625 Combine like terms: 3.75 + 0.390625 = 4.140625 0.390625 + 1.25x + x2 = 4.140625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (x + 0.625) equal to 2.034852575 and -2.034852575.Subproblem 1
x + 0.625 = 2.034852575 Simplifying x + 0.625 = 2.034852575 Reorder the terms: 0.625 + x = 2.034852575 Solving 0.625 + x = 2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 2.034852575 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 2.034852575 + -0.625 x = 2.034852575 + -0.625 Combine like terms: 2.034852575 + -0.625 = 1.409852575 x = 1.409852575 Simplifying x = 1.409852575Subproblem 2
x + 0.625 = -2.034852575 Simplifying x + 0.625 = -2.034852575 Reorder the terms: 0.625 + x = -2.034852575 Solving 0.625 + x = -2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -2.034852575 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -2.034852575 + -0.625 x = -2.034852575 + -0.625 Combine like terms: -2.034852575 + -0.625 = -2.659852575 x = -2.659852575 Simplifying x = -2.659852575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.409852575, -2.659852575}
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