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Simplifying -3x2 + 27x = -40 Reorder the terms: 27x + -3x2 = -40 Solving 27x + -3x2 = -40 Solving for variable 'x'. Reorder the terms: 40 + 27x + -3x2 = -40 + 40 Combine like terms: -40 + 40 = 0 40 + 27x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -13.33333333 + -9x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -9x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -9x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -9x + x2 = 0 + 13.33333333 -9x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -9x + x2 = 13.33333333 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 13.33333333 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 13.33333333 + 20.25 Combine like terms: 13.33333333 + 20.25 = 33.58333333 20.25 + -9x + x2 = 33.58333333 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 33.58333333 Calculate the square root of the right side: 5.795112883 Break this problem into two subproblems by setting (x + -4.5) equal to 5.795112883 and -5.795112883.Subproblem 1
x + -4.5 = 5.795112883 Simplifying x + -4.5 = 5.795112883 Reorder the terms: -4.5 + x = 5.795112883 Solving -4.5 + x = 5.795112883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.795112883 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.795112883 + 4.5 x = 5.795112883 + 4.5 Combine like terms: 5.795112883 + 4.5 = 10.295112883 x = 10.295112883 Simplifying x = 10.295112883Subproblem 2
x + -4.5 = -5.795112883 Simplifying x + -4.5 = -5.795112883 Reorder the terms: -4.5 + x = -5.795112883 Solving -4.5 + x = -5.795112883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.795112883 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.795112883 + 4.5 x = -5.795112883 + 4.5 Combine like terms: -5.795112883 + 4.5 = -1.295112883 x = -1.295112883 Simplifying x = -1.295112883Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.295112883, -1.295112883}
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