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Simplifying 3x2 + 84x + 440 = 1224 Reorder the terms: 440 + 84x + 3x2 = 1224 Solving 440 + 84x + 3x2 = 1224 Solving for variable 'x'. Reorder the terms: 440 + -1224 + 84x + 3x2 = 1224 + -1224 Combine like terms: 440 + -1224 = -784 -784 + 84x + 3x2 = 1224 + -1224 Combine like terms: 1224 + -1224 = 0 -784 + 84x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -261.3333333 + 28x + x2 = 0 Move the constant term to the right: Add '261.3333333' to each side of the equation. -261.3333333 + 28x + 261.3333333 + x2 = 0 + 261.3333333 Reorder the terms: -261.3333333 + 261.3333333 + 28x + x2 = 0 + 261.3333333 Combine like terms: -261.3333333 + 261.3333333 = 0.0000000 0.0000000 + 28x + x2 = 0 + 261.3333333 28x + x2 = 0 + 261.3333333 Combine like terms: 0 + 261.3333333 = 261.3333333 28x + x2 = 261.3333333 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 261.3333333 + 196 Reorder the terms: 196 + 28x + x2 = 261.3333333 + 196 Combine like terms: 261.3333333 + 196 = 457.3333333 196 + 28x + x2 = 457.3333333 Factor a perfect square on the left side: (x + 14)(x + 14) = 457.3333333 Calculate the square root of the right side: 21.385353242 Break this problem into two subproblems by setting (x + 14) equal to 21.385353242 and -21.385353242.Subproblem 1
x + 14 = 21.385353242 Simplifying x + 14 = 21.385353242 Reorder the terms: 14 + x = 21.385353242 Solving 14 + x = 21.385353242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 21.385353242 + -14 Combine like terms: 14 + -14 = 0 0 + x = 21.385353242 + -14 x = 21.385353242 + -14 Combine like terms: 21.385353242 + -14 = 7.385353242 x = 7.385353242 Simplifying x = 7.385353242Subproblem 2
x + 14 = -21.385353242 Simplifying x + 14 = -21.385353242 Reorder the terms: 14 + x = -21.385353242 Solving 14 + x = -21.385353242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -21.385353242 + -14 Combine like terms: 14 + -14 = 0 0 + x = -21.385353242 + -14 x = -21.385353242 + -14 Combine like terms: -21.385353242 + -14 = -35.385353242 x = -35.385353242 Simplifying x = -35.385353242Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.385353242, -35.385353242}
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