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Simplifying 8x2 + 25x + -200 = 0 Reorder the terms: -200 + 25x + 8x2 = 0 Solving -200 + 25x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -25 + 3.125x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 3.125x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 3.125x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 3.125x + x2 = 0 + 25 3.125x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 3.125x + x2 = 25 The x term is 3.125x. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125x + 2.44140625 + x2 = 25 + 2.44140625 Reorder the terms: 2.44140625 + 3.125x + x2 = 25 + 2.44140625 Combine like terms: 25 + 2.44140625 = 27.44140625 2.44140625 + 3.125x + x2 = 27.44140625 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = 27.44140625 Calculate the square root of the right side: 5.238454567 Break this problem into two subproblems by setting (x + 1.5625) equal to 5.238454567 and -5.238454567.Subproblem 1
x + 1.5625 = 5.238454567 Simplifying x + 1.5625 = 5.238454567 Reorder the terms: 1.5625 + x = 5.238454567 Solving 1.5625 + x = 5.238454567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = 5.238454567 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 5.238454567 + -1.5625 x = 5.238454567 + -1.5625 Combine like terms: 5.238454567 + -1.5625 = 3.675954567 x = 3.675954567 Simplifying x = 3.675954567Subproblem 2
x + 1.5625 = -5.238454567 Simplifying x + 1.5625 = -5.238454567 Reorder the terms: 1.5625 + x = -5.238454567 Solving 1.5625 + x = -5.238454567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = -5.238454567 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -5.238454567 + -1.5625 x = -5.238454567 + -1.5625 Combine like terms: -5.238454567 + -1.5625 = -6.800954567 x = -6.800954567 Simplifying x = -6.800954567Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.675954567, -6.800954567}
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