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Simplifying 30x2 + -9x + -4000 = 0 Reorder the terms: -4000 + -9x + 30x2 = 0 Solving -4000 + -9x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -133.3333333 + -0.3x + x2 = 0 Move the constant term to the right: Add '133.3333333' to each side of the equation. -133.3333333 + -0.3x + 133.3333333 + x2 = 0 + 133.3333333 Reorder the terms: -133.3333333 + 133.3333333 + -0.3x + x2 = 0 + 133.3333333 Combine like terms: -133.3333333 + 133.3333333 = 0.0000000 0.0000000 + -0.3x + x2 = 0 + 133.3333333 -0.3x + x2 = 0 + 133.3333333 Combine like terms: 0 + 133.3333333 = 133.3333333 -0.3x + x2 = 133.3333333 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 133.3333333 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 133.3333333 + 0.0225 Combine like terms: 133.3333333 + 0.0225 = 133.3558333 0.0225 + -0.3x + x2 = 133.3558333 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 133.3558333 Calculate the square root of the right side: 11.54797962 Break this problem into two subproblems by setting (x + -0.15) equal to 11.54797962 and -11.54797962.Subproblem 1
x + -0.15 = 11.54797962 Simplifying x + -0.15 = 11.54797962 Reorder the terms: -0.15 + x = 11.54797962 Solving -0.15 + x = 11.54797962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 11.54797962 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 11.54797962 + 0.15 x = 11.54797962 + 0.15 Combine like terms: 11.54797962 + 0.15 = 11.69797962 x = 11.69797962 Simplifying x = 11.69797962Subproblem 2
x + -0.15 = -11.54797962 Simplifying x + -0.15 = -11.54797962 Reorder the terms: -0.15 + x = -11.54797962 Solving -0.15 + x = -11.54797962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -11.54797962 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -11.54797962 + 0.15 x = -11.54797962 + 0.15 Combine like terms: -11.54797962 + 0.15 = -11.39797962 x = -11.39797962 Simplifying x = -11.39797962Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.69797962, -11.39797962}
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