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Simplifying 4x2 + 32x + 33 = 0 Reorder the terms: 33 + 32x + 4x2 = 0 Solving 33 + 32x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.25 + 8x + x2 = 0 Move the constant term to the right: Add '-8.25' to each side of the equation. 8.25 + 8x + -8.25 + x2 = 0 + -8.25 Reorder the terms: 8.25 + -8.25 + 8x + x2 = 0 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + 8x + x2 = 0 + -8.25 8x + x2 = 0 + -8.25 Combine like terms: 0 + -8.25 = -8.25 8x + x2 = -8.25 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -8.25 + 16 Reorder the terms: 16 + 8x + x2 = -8.25 + 16 Combine like terms: -8.25 + 16 = 7.75 16 + 8x + x2 = 7.75 Factor a perfect square on the left side: (x + 4)(x + 4) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + 4) equal to 2.783882181 and -2.783882181.Subproblem 1
x + 4 = 2.783882181 Simplifying x + 4 = 2.783882181 Reorder the terms: 4 + x = 2.783882181 Solving 4 + x = 2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 2.783882181 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.783882181 + -4 x = 2.783882181 + -4 Combine like terms: 2.783882181 + -4 = -1.216117819 x = -1.216117819 Simplifying x = -1.216117819Subproblem 2
x + 4 = -2.783882181 Simplifying x + 4 = -2.783882181 Reorder the terms: 4 + x = -2.783882181 Solving 4 + x = -2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -2.783882181 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.783882181 + -4 x = -2.783882181 + -4 Combine like terms: -2.783882181 + -4 = -6.783882181 x = -6.783882181 Simplifying x = -6.783882181Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.216117819, -6.783882181}
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