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Simplifying -3x2 + 4x + 405 = 0 Reorder the terms: 405 + 4x + -3x2 = 0 Solving 405 + 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'. -135 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '135' to each side of the equation. -135 + -1.333333333x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + -1.333333333x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -1.333333333x + x2 = 0 + 135 -1.333333333x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 -1.333333333x + x2 = 135 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 = 135 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 135 + 0.4444444442 Combine like terms: 135 + 0.4444444442 = 135.4444444442 0.4444444442 + -1.333333333x + x2 = 135.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 135.4444444442 Calculate the square root of the right side: 11.638060167 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 11.638060167 and -11.638060167.Subproblem 1
x + -0.6666666665 = 11.638060167 Simplifying x + -0.6666666665 = 11.638060167 Reorder the terms: -0.6666666665 + x = 11.638060167 Solving -0.6666666665 + x = 11.638060167 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 = 11.638060167 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 11.638060167 + 0.6666666665 x = 11.638060167 + 0.6666666665 Combine like terms: 11.638060167 + 0.6666666665 = 12.3047268335 x = 12.3047268335 Simplifying x = 12.3047268335Subproblem 2
x + -0.6666666665 = -11.638060167 Simplifying x + -0.6666666665 = -11.638060167 Reorder the terms: -0.6666666665 + x = -11.638060167 Solving -0.6666666665 + x = -11.638060167 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 = -11.638060167 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -11.638060167 + 0.6666666665 x = -11.638060167 + 0.6666666665 Combine like terms: -11.638060167 + 0.6666666665 = -10.9713935005 x = -10.9713935005 Simplifying x = -10.9713935005Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.3047268335, -10.9713935005}
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