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Simplifying 0 = -9x2 + 5x + 9 Reorder the terms: 0 = 9 + 5x + -9x2 Solving 0 = 9 + 5x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -5x + 9x2 = 9 + 5x + -9x2 + -9 + -5x + 9x2 Reorder the terms: -9 + -5x + 9x2 = 9 + -9 + 5x + -5x + -9x2 + 9x2 Combine like terms: 9 + -9 = 0 -9 + -5x + 9x2 = 0 + 5x + -5x + -9x2 + 9x2 -9 + -5x + 9x2 = 5x + -5x + -9x2 + 9x2 Combine like terms: 5x + -5x = 0 -9 + -5x + 9x2 = 0 + -9x2 + 9x2 -9 + -5x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -9 + -5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5555555556x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.5555555556x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5555555556x + x2 = 0 + 1 -0.5555555556x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5555555556x + x2 = 1 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 = 1 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 1 + 0.07716049384 Combine like terms: 1 + 0.07716049384 = 1.07716049384 0.07716049384 + -0.5555555556x + x2 = 1.07716049384 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 1.07716049384 Calculate the square root of the right side: 1.037863427 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 1.037863427 and -1.037863427.Subproblem 1
x + -0.2777777778 = 1.037863427 Simplifying x + -0.2777777778 = 1.037863427 Reorder the terms: -0.2777777778 + x = 1.037863427 Solving -0.2777777778 + x = 1.037863427 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 = 1.037863427 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 1.037863427 + 0.2777777778 x = 1.037863427 + 0.2777777778 Combine like terms: 1.037863427 + 0.2777777778 = 1.3156412048 x = 1.3156412048 Simplifying x = 1.3156412048Subproblem 2
x + -0.2777777778 = -1.037863427 Simplifying x + -0.2777777778 = -1.037863427 Reorder the terms: -0.2777777778 + x = -1.037863427 Solving -0.2777777778 + x = -1.037863427 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 = -1.037863427 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -1.037863427 + 0.2777777778 x = -1.037863427 + 0.2777777778 Combine like terms: -1.037863427 + 0.2777777778 = -0.7600856492 x = -0.7600856492 Simplifying x = -0.7600856492Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3156412048, -0.7600856492}
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