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Simplifying 11x2 + 13x + 9 = 11 Reorder the terms: 9 + 13x + 11x2 = 11 Solving 9 + 13x + 11x2 = 11 Solving for variable 'x'. Reorder the terms: 9 + -11 + 13x + 11x2 = 11 + -11 Combine like terms: 9 + -11 = -2 -2 + 13x + 11x2 = 11 + -11 Combine like terms: 11 + -11 = 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 = 0.137782706 x = 0.137782706 Simplifying x = 0.137782706Subproblem 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 = -1.319600888 x = -1.319600888 Simplifying x = -1.319600888Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.137782706, -1.319600888}
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