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Simplifying -0.008x2 + -0.88x + 5 = 0 Reorder the terms: 5 + -0.88x + -0.008x2 = 0 Solving 5 + -0.88x + -0.008x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.008 the coefficient of the squared term: Divide each side by '-0.008'. -625 + 110x + x2 = 0 Move the constant term to the right: Add '625' to each side of the equation. -625 + 110x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + 110x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + 110x + x2 = 0 + 625 110x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 110x + x2 = 625 The x term is 110x. Take half its coefficient (55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. 110x + 3025 + x2 = 625 + 3025 Reorder the terms: 3025 + 110x + x2 = 625 + 3025 Combine like terms: 625 + 3025 = 3650 3025 + 110x + x2 = 3650 Factor a perfect square on the left side: (x + 55)(x + 55) = 3650 Calculate the square root of the right side: 60.415229868 Break this problem into two subproblems by setting (x + 55) equal to 60.415229868 and -60.415229868.Subproblem 1
x + 55 = 60.415229868 Simplifying x + 55 = 60.415229868 Reorder the terms: 55 + x = 60.415229868 Solving 55 + x = 60.415229868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = 60.415229868 + -55 Combine like terms: 55 + -55 = 0 0 + x = 60.415229868 + -55 x = 60.415229868 + -55 Combine like terms: 60.415229868 + -55 = 5.415229868 x = 5.415229868 Simplifying x = 5.415229868Subproblem 2
x + 55 = -60.415229868 Simplifying x + 55 = -60.415229868 Reorder the terms: 55 + x = -60.415229868 Solving 55 + x = -60.415229868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = -60.415229868 + -55 Combine like terms: 55 + -55 = 0 0 + x = -60.415229868 + -55 x = -60.415229868 + -55 Combine like terms: -60.415229868 + -55 = -115.415229868 x = -115.415229868 Simplifying x = -115.415229868Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.415229868, -115.415229868}
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