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Simplifying 9x2 + 9x = 7 Reorder the terms: 9x + 9x2 = 7 Solving 9x + 9x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 9x + 9x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 9x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.7777777778 x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 x + x2 = 0.7777777778 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.7777777778 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.7777777778 + 0.25 Combine like terms: 0.7777777778 + 0.25 = 1.0277777778 1.25 + x2 = 1.0277777778 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.0277777778 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (x + 0.5) equal to 1.013793755 and -1.013793755.Subproblem 1
x + 0.5 = 1.013793755 Simplifying x + 0.5 = 1.013793755 Reorder the terms: 0.5 + x = 1.013793755 Solving 0.5 + x = 1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.013793755 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.013793755 + -0.5 x = 1.013793755 + -0.5 Combine like terms: 1.013793755 + -0.5 = 0.513793755 x = 0.513793755 Simplifying x = 0.513793755Subproblem 2
x + 0.5 = -1.013793755 Simplifying x + 0.5 = -1.013793755 Reorder the terms: 0.5 + x = -1.013793755 Solving 0.5 + x = -1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.013793755 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.013793755 + -0.5 x = -1.013793755 + -0.5 Combine like terms: -1.013793755 + -0.5 = -1.513793755 x = -1.513793755 Simplifying x = -1.513793755Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.513793755, -1.513793755}
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