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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 Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 27x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40 + 27x + 3x2)' equal to zero and attempt to solve: Simplifying 40 + 27x + 3x2 = 0 Solving 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 = 6.91666667 20.25 + 9x + x2 = 6.91666667 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 6.91666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (x + 4.5) equal to 2.62995564 and -2.62995564.Subproblem 1
x + 4.5 = 2.62995564 Simplifying x + 4.5 = 2.62995564 Reorder the terms: 4.5 + x = 2.62995564 Solving 4.5 + x = 2.62995564 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 = 2.62995564 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 2.62995564 + -4.5 x = 2.62995564 + -4.5 Combine like terms: 2.62995564 + -4.5 = -1.87004436 x = -1.87004436 Simplifying x = -1.87004436Subproblem 2
x + 4.5 = -2.62995564 Simplifying x + 4.5 = -2.62995564 Reorder the terms: 4.5 + x = -2.62995564 Solving 4.5 + x = -2.62995564 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 = -2.62995564 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -2.62995564 + -4.5 x = -2.62995564 + -4.5 Combine like terms: -2.62995564 + -4.5 = -7.12995564 x = -7.12995564 Simplifying x = -7.12995564Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.87004436, -7.12995564}Solution
x = {-1.87004436, -7.12995564}
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