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Simplifying 9x2 + 5x + -25 = 0 Reorder the terms: -25 + 5x + 9x2 = 0 Solving -25 + 5x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.777777778 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + 0.5555555556x + 2.777777778 + x2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + 0.5555555556x + x2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + 0.5555555556x + x2 = 0 + 2.777777778 0.5555555556x + x2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 0.5555555556x + x2 = 2.777777778 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 2.777777778 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 2.777777778 + 0.07716049384 Combine like terms: 2.777777778 + 0.07716049384 = 2.85493827184 0.07716049384 + 0.5555555556x + x2 = 2.85493827184 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 2.85493827184 Calculate the square root of the right side: 1.689656258 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 1.689656258 and -1.689656258.Subproblem 1
x + 0.2777777778 = 1.689656258 Simplifying x + 0.2777777778 = 1.689656258 Reorder the terms: 0.2777777778 + x = 1.689656258 Solving 0.2777777778 + x = 1.689656258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 1.689656258 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 1.689656258 + -0.2777777778 x = 1.689656258 + -0.2777777778 Combine like terms: 1.689656258 + -0.2777777778 = 1.4118784802 x = 1.4118784802 Simplifying x = 1.4118784802Subproblem 2
x + 0.2777777778 = -1.689656258 Simplifying x + 0.2777777778 = -1.689656258 Reorder the terms: 0.2777777778 + x = -1.689656258 Solving 0.2777777778 + x = -1.689656258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -1.689656258 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -1.689656258 + -0.2777777778 x = -1.689656258 + -0.2777777778 Combine like terms: -1.689656258 + -0.2777777778 = -1.9674340358 x = -1.9674340358 Simplifying x = -1.9674340358Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4118784802, -1.9674340358}
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