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Simplifying 2x2 + -33x + 72 = 0 Reorder the terms: 72 + -33x + 2x2 = 0 Solving 72 + -33x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 36 + -16.5x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -16.5x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -16.5x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -16.5x + x2 = 0 + -36 -16.5x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -16.5x + x2 = -36 The x term is -16.5x. Take half its coefficient (-8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. -16.5x + 68.0625 + x2 = -36 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = -36 + 68.0625 Combine like terms: -36 + 68.0625 = 32.0625 68.0625 + -16.5x + x2 = 32.0625 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 32.0625 Calculate the square root of the right side: 5.662375826 Break this problem into two subproblems by setting (x + -8.25) equal to 5.662375826 and -5.662375826.Subproblem 1
x + -8.25 = 5.662375826 Simplifying x + -8.25 = 5.662375826 Reorder the terms: -8.25 + x = 5.662375826 Solving -8.25 + x = 5.662375826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = 5.662375826 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 5.662375826 + 8.25 x = 5.662375826 + 8.25 Combine like terms: 5.662375826 + 8.25 = 13.912375826 x = 13.912375826 Simplifying x = 13.912375826Subproblem 2
x + -8.25 = -5.662375826 Simplifying x + -8.25 = -5.662375826 Reorder the terms: -8.25 + x = -5.662375826 Solving -8.25 + x = -5.662375826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = -5.662375826 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -5.662375826 + 8.25 x = -5.662375826 + 8.25 Combine like terms: -5.662375826 + 8.25 = 2.587624174 x = 2.587624174 Simplifying x = 2.587624174Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.912375826, 2.587624174}
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