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Simplifying 2x2 + -11x + 2 = 64 Reorder the terms: 2 + -11x + 2x2 = 64 Solving 2 + -11x + 2x2 = 64 Solving for variable 'x'. Reorder the terms: 2 + -64 + -11x + 2x2 = 64 + -64 Combine like terms: 2 + -64 = -62 -62 + -11x + 2x2 = 64 + -64 Combine like terms: 64 + -64 = 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 = 8.959871174 x = 8.959871174 Simplifying x = 8.959871174Subproblem 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 = -3.459871174 x = -3.459871174 Simplifying x = -3.459871174Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.959871174, -3.459871174}
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