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Simplifying 9x2 + 5x = 9x + 16 Reorder the terms: 5x + 9x2 = 9x + 16 Reorder the terms: 5x + 9x2 = 16 + 9x Solving 5x + 9x2 = 16 + 9x Solving for variable 'x'. Reorder the terms: -16 + 5x + -9x + 9x2 = 16 + 9x + -16 + -9x Combine like terms: 5x + -9x = -4x -16 + -4x + 9x2 = 16 + 9x + -16 + -9x Reorder the terms: -16 + -4x + 9x2 = 16 + -16 + 9x + -9x Combine like terms: 16 + -16 = 0 -16 + -4x + 9x2 = 0 + 9x + -9x -16 + -4x + 9x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -16 + -4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -0.4444444444x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -0.4444444444x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -0.4444444444x + x2 = 0 + 1.777777778 -0.4444444444x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -0.4444444444x + x2 = 1.777777778 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 1.777777778 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 1.777777778 + 0.04938271604 Combine like terms: 1.777777778 + 0.04938271604 = 1.82716049404 0.04938271604 + -0.4444444444x + x2 = 1.82716049404 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 1.82716049404 Calculate the square root of the right side: 1.351725007 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 1.351725007 and -1.351725007.Subproblem 1
x + -0.2222222222 = 1.351725007 Simplifying x + -0.2222222222 = 1.351725007 Reorder the terms: -0.2222222222 + x = 1.351725007 Solving -0.2222222222 + x = 1.351725007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 1.351725007 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 1.351725007 + 0.2222222222 x = 1.351725007 + 0.2222222222 Combine like terms: 1.351725007 + 0.2222222222 = 1.5739472292 x = 1.5739472292 Simplifying x = 1.5739472292Subproblem 2
x + -0.2222222222 = -1.351725007 Simplifying x + -0.2222222222 = -1.351725007 Reorder the terms: -0.2222222222 + x = -1.351725007 Solving -0.2222222222 + x = -1.351725007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -1.351725007 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -1.351725007 + 0.2222222222 x = -1.351725007 + 0.2222222222 Combine like terms: -1.351725007 + 0.2222222222 = -1.1295027848 x = -1.1295027848 Simplifying x = -1.1295027848Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5739472292, -1.1295027848}
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