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Simplifying 9x2 + 12 = 37 + 5x Reorder the terms: 12 + 9x2 = 37 + 5x Solving 12 + 9x2 = 37 + 5x Solving for variable 'x'. Reorder the terms: 12 + -37 + -5x + 9x2 = 37 + 5x + -37 + -5x Combine like terms: 12 + -37 = -25 -25 + -5x + 9x2 = 37 + 5x + -37 + -5x Reorder the terms: -25 + -5x + 9x2 = 37 + -37 + 5x + -5x Combine like terms: 37 + -37 = 0 -25 + -5x + 9x2 = 0 + 5x + -5x -25 + -5x + 9x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -25 + -5x + 9x2 = 0 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 = 1.9674340358 x = 1.9674340358 Simplifying x = 1.9674340358Subproblem 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 = -1.4118784802 x = -1.4118784802 Simplifying x = -1.4118784802Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9674340358, -1.4118784802}
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