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Simplifying 2x2 + 33x + -9.1 = 0 Reorder the terms: -9.1 + 33x + 2x2 = 0 Solving -9.1 + 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'. -4.55 + 16.5x + x2 = 0 Move the constant term to the right: Add '4.55' to each side of the equation. -4.55 + 16.5x + 4.55 + x2 = 0 + 4.55 Reorder the terms: -4.55 + 4.55 + 16.5x + x2 = 0 + 4.55 Combine like terms: -4.55 + 4.55 = 0.00 0.00 + 16.5x + x2 = 0 + 4.55 16.5x + x2 = 0 + 4.55 Combine like terms: 0 + 4.55 = 4.55 16.5x + x2 = 4.55 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 = 4.55 + 68.0625 Reorder the terms: 68.0625 + 16.5x + x2 = 4.55 + 68.0625 Combine like terms: 4.55 + 68.0625 = 72.6125 68.0625 + 16.5x + x2 = 72.6125 Factor a perfect square on the left side: (x + 8.25)(x + 8.25) = 72.6125 Calculate the square root of the right side: 8.52129685 Break this problem into two subproblems by setting (x + 8.25) equal to 8.52129685 and -8.52129685.Subproblem 1
x + 8.25 = 8.52129685 Simplifying x + 8.25 = 8.52129685 Reorder the terms: 8.25 + x = 8.52129685 Solving 8.25 + x = 8.52129685 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 = 8.52129685 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = 8.52129685 + -8.25 x = 8.52129685 + -8.25 Combine like terms: 8.52129685 + -8.25 = 0.27129685 x = 0.27129685 Simplifying x = 0.27129685Subproblem 2
x + 8.25 = -8.52129685 Simplifying x + 8.25 = -8.52129685 Reorder the terms: 8.25 + x = -8.52129685 Solving 8.25 + x = -8.52129685 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 = -8.52129685 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = -8.52129685 + -8.25 x = -8.52129685 + -8.25 Combine like terms: -8.52129685 + -8.25 = -16.77129685 x = -16.77129685 Simplifying x = -16.77129685Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.27129685, -16.77129685}
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