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Simplifying -2 = -11X2 + 13X Reorder the terms: -2 = 13X + -11X2 Solving -2 = 13X + -11X2 Solving for variable 'X'. Reorder the terms: -2 + -13X + 11X2 = 13X + -13X + -11X2 + 11X2 Combine like terms: 13X + -13X = 0 -2 + -13X + 11X2 = 0 + -11X2 + 11X2 -2 + -13X + 11X2 = -11X2 + 11X2 Combine like terms: -11X2 + 11X2 = 0 -2 + -13X + 11X2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + -1.181818182X + X2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -1.181818182X + 0.1818181818 + X2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -1.181818182X + X2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -1.181818182X + X2 = 0 + 0.1818181818 -1.181818182X + X2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -1.181818182X + X2 = 0.1818181818 The X term is -1.181818182X. Take half its coefficient (-0.590909091). Square it (0.3491735538) and add it to both sides. Add '0.3491735538' to each side of the equation. -1.181818182X + 0.3491735538 + X2 = 0.1818181818 + 0.3491735538 Reorder the terms: 0.3491735538 + -1.181818182X + X2 = 0.1818181818 + 0.3491735538 Combine like terms: 0.1818181818 + 0.3491735538 = 0.5309917356 0.3491735538 + -1.181818182X + X2 = 0.5309917356 Factor a perfect square on the left side: (X + -0.590909091)(X + -0.590909091) = 0.5309917356 Calculate the square root of the right side: 0.728691797 Break this problem into two subproblems by setting (X + -0.590909091) equal to 0.728691797 and -0.728691797.Subproblem 1
X + -0.590909091 = 0.728691797 Simplifying X + -0.590909091 = 0.728691797 Reorder the terms: -0.590909091 + X = 0.728691797 Solving -0.590909091 + X = 0.728691797 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.590909091' to each side of the equation. -0.590909091 + 0.590909091 + X = 0.728691797 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + X = 0.728691797 + 0.590909091 X = 0.728691797 + 0.590909091 Combine like terms: 0.728691797 + 0.590909091 = 1.319600888 X = 1.319600888 Simplifying X = 1.319600888Subproblem 2
X + -0.590909091 = -0.728691797 Simplifying X + -0.590909091 = -0.728691797 Reorder the terms: -0.590909091 + X = -0.728691797 Solving -0.590909091 + X = -0.728691797 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.590909091' to each side of the equation. -0.590909091 + 0.590909091 + X = -0.728691797 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + X = -0.728691797 + 0.590909091 X = -0.728691797 + 0.590909091 Combine like terms: -0.728691797 + 0.590909091 = -0.137782706 X = -0.137782706 Simplifying X = -0.137782706Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.319600888, -0.137782706}
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