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Simplifying -9x2 + -6x + 7 = 0 Reorder the terms: 7 + -6x + -9x2 = 0 Solving 7 + -6x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.7777777778 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 0.6666666667x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 0.6666666667x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + 0.7777777778 0.6666666667x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 0.6666666667x + x2 = 0.7777777778 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.7777777778 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.7777777778 + 0.1111111112 Combine like terms: 0.7777777778 + 0.1111111112 = 0.888888889 0.1111111112 + 0.6666666667x + x2 = 0.888888889 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.888888889 Calculate the square root of the right side: 0.942809042 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.942809042 and -0.942809042.Subproblem 1
x + 0.3333333334 = 0.942809042 Simplifying x + 0.3333333334 = 0.942809042 Reorder the terms: 0.3333333334 + x = 0.942809042 Solving 0.3333333334 + x = 0.942809042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.942809042 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.942809042 + -0.3333333334 x = 0.942809042 + -0.3333333334 Combine like terms: 0.942809042 + -0.3333333334 = 0.6094757086 x = 0.6094757086 Simplifying x = 0.6094757086Subproblem 2
x + 0.3333333334 = -0.942809042 Simplifying x + 0.3333333334 = -0.942809042 Reorder the terms: 0.3333333334 + x = -0.942809042 Solving 0.3333333334 + x = -0.942809042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.942809042 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.942809042 + -0.3333333334 x = -0.942809042 + -0.3333333334 Combine like terms: -0.942809042 + -0.3333333334 = -1.2761423754 x = -1.2761423754 Simplifying x = -1.2761423754Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6094757086, -1.2761423754}
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