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Simplifying -2x2 + -55x + 121 = 12 Reorder the terms: 121 + -55x + -2x2 = 12 Solving 121 + -55x + -2x2 = 12 Solving for variable 'x'. Reorder the terms: 121 + -12 + -55x + -2x2 = 12 + -12 Combine like terms: 121 + -12 = 109 109 + -55x + -2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 109 + -55x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -54.5 + 27.5x + x2 = 0 Move the constant term to the right: Add '54.5' to each side of the equation. -54.5 + 27.5x + 54.5 + x2 = 0 + 54.5 Reorder the terms: -54.5 + 54.5 + 27.5x + x2 = 0 + 54.5 Combine like terms: -54.5 + 54.5 = 0.0 0.0 + 27.5x + x2 = 0 + 54.5 27.5x + x2 = 0 + 54.5 Combine like terms: 0 + 54.5 = 54.5 27.5x + x2 = 54.5 The x term is 27.5x. Take half its coefficient (13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. 27.5x + 189.0625 + x2 = 54.5 + 189.0625 Reorder the terms: 189.0625 + 27.5x + x2 = 54.5 + 189.0625 Combine like terms: 54.5 + 189.0625 = 243.5625 189.0625 + 27.5x + x2 = 243.5625 Factor a perfect square on the left side: (x + 13.75)(x + 13.75) = 243.5625 Calculate the square root of the right side: 15.606489035 Break this problem into two subproblems by setting (x + 13.75) equal to 15.606489035 and -15.606489035.Subproblem 1
x + 13.75 = 15.606489035 Simplifying x + 13.75 = 15.606489035 Reorder the terms: 13.75 + x = 15.606489035 Solving 13.75 + x = 15.606489035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = 15.606489035 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = 15.606489035 + -13.75 x = 15.606489035 + -13.75 Combine like terms: 15.606489035 + -13.75 = 1.856489035 x = 1.856489035 Simplifying x = 1.856489035Subproblem 2
x + 13.75 = -15.606489035 Simplifying x + 13.75 = -15.606489035 Reorder the terms: 13.75 + x = -15.606489035 Solving 13.75 + x = -15.606489035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = -15.606489035 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = -15.606489035 + -13.75 x = -15.606489035 + -13.75 Combine like terms: -15.606489035 + -13.75 = -29.356489035 x = -29.356489035 Simplifying x = -29.356489035Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.856489035, -29.356489035}
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