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Simplifying 0 = 2x2 + -11x + -14 Reorder the terms: 0 = -14 + -11x + 2x2 Solving 0 = -14 + -11x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 14 = 14 14 + 11x + -2x2 = -14 + -11x + 2x2 + 14 + 11x + -2x2 Reorder the terms: 14 + 11x + -2x2 = -14 + 14 + -11x + 11x + 2x2 + -2x2 Combine like terms: -14 + 14 = 0 14 + 11x + -2x2 = 0 + -11x + 11x + 2x2 + -2x2 14 + 11x + -2x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 14 + 11x + -2x2 = 0 + 2x2 + -2x2 14 + 11x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 14 + 11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7 + -5.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -5.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -5.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5.5x + x2 = 0 + 7 -5.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5.5x + x2 = 7 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 = 7 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 7 + 7.5625 Combine like terms: 7 + 7.5625 = 14.5625 7.5625 + -5.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + -2.75) equal to 3.816084381 and -3.816084381.Subproblem 1
x + -2.75 = 3.816084381 Simplifying x + -2.75 = 3.816084381 Reorder the terms: -2.75 + x = 3.816084381 Solving -2.75 + x = 3.816084381 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 = 3.816084381 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.816084381 + 2.75 x = 3.816084381 + 2.75 Combine like terms: 3.816084381 + 2.75 = 6.566084381 x = 6.566084381 Simplifying x = 6.566084381Subproblem 2
x + -2.75 = -3.816084381 Simplifying x + -2.75 = -3.816084381 Reorder the terms: -2.75 + x = -3.816084381 Solving -2.75 + x = -3.816084381 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 = -3.816084381 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.816084381 + 2.75 x = -3.816084381 + 2.75 Combine like terms: -3.816084381 + 2.75 = -1.066084381 x = -1.066084381 Simplifying x = -1.066084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.566084381, -1.066084381}
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