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Simplifying 0 = -6x2 + 8x + 9 Reorder the terms: 0 = 9 + 8x + -6x2 Solving 0 = 9 + 8x + -6x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -8x + 6x2 = 9 + 8x + -6x2 + -9 + -8x + 6x2 Reorder the terms: -9 + -8x + 6x2 = 9 + -9 + 8x + -8x + -6x2 + 6x2 Combine like terms: 9 + -9 = 0 -9 + -8x + 6x2 = 0 + 8x + -8x + -6x2 + 6x2 -9 + -8x + 6x2 = 8x + -8x + -6x2 + 6x2 Combine like terms: 8x + -8x = 0 -9 + -8x + 6x2 = 0 + -6x2 + 6x2 -9 + -8x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -9 + -8x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1.333333333x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1.333333333x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1.333333333x + x2 = 0 + 1.5 -1.333333333x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1.333333333x + x2 = 1.5 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 = 1.5 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 1.5 + 0.4444444442 Combine like terms: 1.5 + 0.4444444442 = 1.9444444442 0.4444444442 + -1.333333333x + x2 = 1.9444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 1.9444444442 Calculate the square root of the right side: 1.394433377 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.394433377 and -1.394433377.Subproblem 1
x + -0.6666666665 = 1.394433377 Simplifying x + -0.6666666665 = 1.394433377 Reorder the terms: -0.6666666665 + x = 1.394433377 Solving -0.6666666665 + x = 1.394433377 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 = 1.394433377 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.394433377 + 0.6666666665 x = 1.394433377 + 0.6666666665 Combine like terms: 1.394433377 + 0.6666666665 = 2.0611000435 x = 2.0611000435 Simplifying x = 2.0611000435Subproblem 2
x + -0.6666666665 = -1.394433377 Simplifying x + -0.6666666665 = -1.394433377 Reorder the terms: -0.6666666665 + x = -1.394433377 Solving -0.6666666665 + x = -1.394433377 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 = -1.394433377 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.394433377 + 0.6666666665 x = -1.394433377 + 0.6666666665 Combine like terms: -1.394433377 + 0.6666666665 = -0.7277667105 x = -0.7277667105 Simplifying x = -0.7277667105Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0611000435, -0.7277667105}
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