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Simplifying -11x + 62 = 2x2 Reorder the terms: 62 + -11x = 2x2 Solving 62 + -11x = 2x2 Solving for variable 'x'. Combine like terms: 2x2 + -2x2 = 0 62 + -11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -31 + 5.5x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 5.5x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 5.5x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 5.5x + x2 = 0 + 31 5.5x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 5.5x + x2 = 31 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 31 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 31 + 7.5625 Combine like terms: 31 + 7.5625 = 38.5625 7.5625 + 5.5x + x2 = 38.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 38.5625 Calculate the square root of the right side: 6.209871174 Break this problem into two subproblems by setting (x + 2.75) equal to 6.209871174 and -6.209871174.Subproblem 1
x + 2.75 = 6.209871174 Simplifying x + 2.75 = 6.209871174 Reorder the terms: 2.75 + x = 6.209871174 Solving 2.75 + x = 6.209871174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 6.209871174 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 6.209871174 + -2.75 x = 6.209871174 + -2.75 Combine like terms: 6.209871174 + -2.75 = 3.459871174 x = 3.459871174 Simplifying x = 3.459871174Subproblem 2
x + 2.75 = -6.209871174 Simplifying x + 2.75 = -6.209871174 Reorder the terms: 2.75 + x = -6.209871174 Solving 2.75 + x = -6.209871174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -6.209871174 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -6.209871174 + -2.75 x = -6.209871174 + -2.75 Combine like terms: -6.209871174 + -2.75 = -8.959871174 x = -8.959871174 Simplifying x = -8.959871174Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.459871174, -8.959871174}
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