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Simplifying 9x(x) = 7 + -5x Multiply x * x 9x2 = 7 + -5x Solving 9x2 = 7 + -5x Solving for variable 'x'. Reorder the terms: -7 + 5x + 9x2 = 7 + -5x + -7 + 5x Reorder the terms: -7 + 5x + 9x2 = 7 + -7 + -5x + 5x Combine like terms: 7 + -7 = 0 -7 + 5x + 9x2 = 0 + -5x + 5x -7 + 5x + 9x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -7 + 5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 0.5555555556x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 0.5555555556x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 0.5555555556x + x2 = 0 + 0.7777777778 0.5555555556x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 0.5555555556x + x2 = 0.7777777778 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 = 0.7777777778 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 0.7777777778 + 0.07716049384 Combine like terms: 0.7777777778 + 0.07716049384 = 0.85493827164 0.07716049384 + 0.5555555556x + x2 = 0.85493827164 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 0.85493827164 Calculate the square root of the right side: 0.924628721 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 0.924628721 and -0.924628721.Subproblem 1
x + 0.2777777778 = 0.924628721 Simplifying x + 0.2777777778 = 0.924628721 Reorder the terms: 0.2777777778 + x = 0.924628721 Solving 0.2777777778 + x = 0.924628721 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 = 0.924628721 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 0.924628721 + -0.2777777778 x = 0.924628721 + -0.2777777778 Combine like terms: 0.924628721 + -0.2777777778 = 0.6468509432 x = 0.6468509432 Simplifying x = 0.6468509432Subproblem 2
x + 0.2777777778 = -0.924628721 Simplifying x + 0.2777777778 = -0.924628721 Reorder the terms: 0.2777777778 + x = -0.924628721 Solving 0.2777777778 + x = -0.924628721 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 = -0.924628721 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -0.924628721 + -0.2777777778 x = -0.924628721 + -0.2777777778 Combine like terms: -0.924628721 + -0.2777777778 = -1.2024064988 x = -1.2024064988 Simplifying x = -1.2024064988Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6468509432, -1.2024064988}
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