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Simplifying 11x2 + 13x + -72 = 1 Reorder the terms: -72 + 13x + 11x2 = 1 Solving -72 + 13x + 11x2 = 1 Solving for variable 'x'. Reorder the terms: -72 + -1 + 13x + 11x2 = 1 + -1 Combine like terms: -72 + -1 = -73 -73 + 13x + 11x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -73 + 13x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -6.636363636 + 1.181818182x + x2 = 0 Move the constant term to the right: Add '6.636363636' to each side of the equation. -6.636363636 + 1.181818182x + 6.636363636 + x2 = 0 + 6.636363636 Reorder the terms: -6.636363636 + 6.636363636 + 1.181818182x + x2 = 0 + 6.636363636 Combine like terms: -6.636363636 + 6.636363636 = 0.000000000 0.000000000 + 1.181818182x + x2 = 0 + 6.636363636 1.181818182x + x2 = 0 + 6.636363636 Combine like terms: 0 + 6.636363636 = 6.636363636 1.181818182x + x2 = 6.636363636 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 = 6.636363636 + 0.3491735538 Reorder the terms: 0.3491735538 + 1.181818182x + x2 = 6.636363636 + 0.3491735538 Combine like terms: 6.636363636 + 0.3491735538 = 6.9855371898 0.3491735538 + 1.181818182x + x2 = 6.9855371898 Factor a perfect square on the left side: (x + 0.590909091)(x + 0.590909091) = 6.9855371898 Calculate the square root of the right side: 2.643016684 Break this problem into two subproblems by setting (x + 0.590909091) equal to 2.643016684 and -2.643016684.Subproblem 1
x + 0.590909091 = 2.643016684 Simplifying x + 0.590909091 = 2.643016684 Reorder the terms: 0.590909091 + x = 2.643016684 Solving 0.590909091 + x = 2.643016684 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 = 2.643016684 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = 2.643016684 + -0.590909091 x = 2.643016684 + -0.590909091 Combine like terms: 2.643016684 + -0.590909091 = 2.052107593 x = 2.052107593 Simplifying x = 2.052107593Subproblem 2
x + 0.590909091 = -2.643016684 Simplifying x + 0.590909091 = -2.643016684 Reorder the terms: 0.590909091 + x = -2.643016684 Solving 0.590909091 + x = -2.643016684 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 = -2.643016684 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = -2.643016684 + -0.590909091 x = -2.643016684 + -0.590909091 Combine like terms: -2.643016684 + -0.590909091 = -3.233925775 x = -3.233925775 Simplifying x = -3.233925775Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.052107593, -3.233925775}
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