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Simplifying 11x2 + -4x + -225 = 0 Reorder the terms: -225 + -4x + 11x2 = 0 Solving -225 + -4x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -20.45454545 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '20.45454545' to each side of the equation. -20.45454545 + -0.3636363636x + 20.45454545 + x2 = 0 + 20.45454545 Reorder the terms: -20.45454545 + 20.45454545 + -0.3636363636x + x2 = 0 + 20.45454545 Combine like terms: -20.45454545 + 20.45454545 = 0.00000000 0.00000000 + -0.3636363636x + x2 = 0 + 20.45454545 -0.3636363636x + x2 = 0 + 20.45454545 Combine like terms: 0 + 20.45454545 = 20.45454545 -0.3636363636x + x2 = 20.45454545 The x term is -0.3636363636x. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636x + 0.03305785123 + x2 = 20.45454545 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 20.45454545 + 0.03305785123 Combine like terms: 20.45454545 + 0.03305785123 = 20.48760330123 0.03305785123 + -0.3636363636x + x2 = 20.48760330123 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 20.48760330123 Calculate the square root of the right side: 4.526323376 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 4.526323376 and -4.526323376.Subproblem 1
x + -0.1818181818 = 4.526323376 Simplifying x + -0.1818181818 = 4.526323376 Reorder the terms: -0.1818181818 + x = 4.526323376 Solving -0.1818181818 + x = 4.526323376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = 4.526323376 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 4.526323376 + 0.1818181818 x = 4.526323376 + 0.1818181818 Combine like terms: 4.526323376 + 0.1818181818 = 4.7081415578 x = 4.7081415578 Simplifying x = 4.7081415578Subproblem 2
x + -0.1818181818 = -4.526323376 Simplifying x + -0.1818181818 = -4.526323376 Reorder the terms: -0.1818181818 + x = -4.526323376 Solving -0.1818181818 + x = -4.526323376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = -4.526323376 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -4.526323376 + 0.1818181818 x = -4.526323376 + 0.1818181818 Combine like terms: -4.526323376 + 0.1818181818 = -4.3445051942 x = -4.3445051942 Simplifying x = -4.3445051942Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.7081415578, -4.3445051942}
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