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Simplifying 0 = 9x2 + 12x + -7 Reorder the terms: 0 = -7 + 12x + 9x2 Solving 0 = -7 + 12x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + -12x + -9x2 = -7 + 12x + 9x2 + 7 + -12x + -9x2 Reorder the terms: 7 + -12x + -9x2 = -7 + 7 + 12x + -12x + 9x2 + -9x2 Combine like terms: -7 + 7 = 0 7 + -12x + -9x2 = 0 + 12x + -12x + 9x2 + -9x2 7 + -12x + -9x2 = 12x + -12x + 9x2 + -9x2 Combine like terms: 12x + -12x = 0 7 + -12x + -9x2 = 0 + 9x2 + -9x2 7 + -12x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 7 + -12x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.7777777778 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 1.333333333x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 1.333333333x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.7777777778 1.333333333x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 1.333333333x + x2 = 0.7777777778 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 0.7777777778 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.7777777778 + 0.4444444442 Combine like terms: 0.7777777778 + 0.4444444442 = 1.222222222 0.4444444442 + 1.333333333x + x2 = 1.222222222 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 1.222222222 Calculate the square root of the right side: 1.105541597 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.105541597 and -1.105541597.Subproblem 1
x + 0.6666666665 = 1.105541597 Simplifying x + 0.6666666665 = 1.105541597 Reorder the terms: 0.6666666665 + x = 1.105541597 Solving 0.6666666665 + x = 1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.105541597 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.105541597 + -0.6666666665 x = 1.105541597 + -0.6666666665 Combine like terms: 1.105541597 + -0.6666666665 = 0.4388749305 x = 0.4388749305 Simplifying x = 0.4388749305Subproblem 2
x + 0.6666666665 = -1.105541597 Simplifying x + 0.6666666665 = -1.105541597 Reorder the terms: 0.6666666665 + x = -1.105541597 Solving 0.6666666665 + x = -1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.105541597 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.105541597 + -0.6666666665 x = -1.105541597 + -0.6666666665 Combine like terms: -1.105541597 + -0.6666666665 = -1.7722082635 x = -1.7722082635 Simplifying x = -1.7722082635Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4388749305, -1.7722082635}
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