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Simplifying 2x2 + 24x + 33 = 0 Reorder the terms: 33 + 24x + 2x2 = 0 Solving 33 + 24x + 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'. 16.5 + 12x + x2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + 12x + -16.5 + x2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + 12x + x2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + 12x + x2 = 0 + -16.5 12x + x2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 12x + x2 = -16.5 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -16.5 + 36 Reorder the terms: 36 + 12x + x2 = -16.5 + 36 Combine like terms: -16.5 + 36 = 19.5 36 + 12x + x2 = 19.5 Factor a perfect square on the left side: (x + 6)(x + 6) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (x + 6) equal to 4.415880433 and -4.415880433.Subproblem 1
x + 6 = 4.415880433 Simplifying x + 6 = 4.415880433 Reorder the terms: 6 + x = 4.415880433 Solving 6 + x = 4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 4.415880433 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.415880433 + -6 x = 4.415880433 + -6 Combine like terms: 4.415880433 + -6 = -1.584119567 x = -1.584119567 Simplifying x = -1.584119567Subproblem 2
x + 6 = -4.415880433 Simplifying x + 6 = -4.415880433 Reorder the terms: 6 + x = -4.415880433 Solving 6 + x = -4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -4.415880433 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.415880433 + -6 x = -4.415880433 + -6 Combine like terms: -4.415880433 + -6 = -10.415880433 x = -10.415880433 Simplifying x = -10.415880433Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.584119567, -10.415880433}
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