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Simplifying 3x2 + 4x + -66 = 0 Reorder the terms: -66 + 4x + 3x2 = 0 Solving -66 + 4x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -22 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 1.333333333x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 1.333333333x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 1.333333333x + x2 = 0 + 22 1.333333333x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 1.333333333x + x2 = 22 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 = 22 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 22 + 0.4444444442 Combine like terms: 22 + 0.4444444442 = 22.4444444442 0.4444444442 + 1.333333333x + x2 = 22.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 22.4444444442 Calculate the square root of the right side: 4.737556801 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 4.737556801 and -4.737556801.Subproblem 1
x + 0.6666666665 = 4.737556801 Simplifying x + 0.6666666665 = 4.737556801 Reorder the terms: 0.6666666665 + x = 4.737556801 Solving 0.6666666665 + x = 4.737556801 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 = 4.737556801 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 4.737556801 + -0.6666666665 x = 4.737556801 + -0.6666666665 Combine like terms: 4.737556801 + -0.6666666665 = 4.0708901345 x = 4.0708901345 Simplifying x = 4.0708901345Subproblem 2
x + 0.6666666665 = -4.737556801 Simplifying x + 0.6666666665 = -4.737556801 Reorder the terms: 0.6666666665 + x = -4.737556801 Solving 0.6666666665 + x = -4.737556801 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 = -4.737556801 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -4.737556801 + -0.6666666665 x = -4.737556801 + -0.6666666665 Combine like terms: -4.737556801 + -0.6666666665 = -5.4042234675 x = -5.4042234675 Simplifying x = -5.4042234675Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.0708901345, -5.4042234675}
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