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Simplifying 22x2 + 18x + -100 = 0 Reorder the terms: -100 + 18x + 22x2 = 0 Solving -100 + 18x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 9x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 9x + 11x2)' equal to zero and attempt to solve: Simplifying -50 + 9x + 11x2 = 0 Solving -50 + 9x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -4.545454545 + 0.8181818182x + x2 = 0 Move the constant term to the right: Add '4.545454545' to each side of the equation. -4.545454545 + 0.8181818182x + 4.545454545 + x2 = 0 + 4.545454545 Reorder the terms: -4.545454545 + 4.545454545 + 0.8181818182x + x2 = 0 + 4.545454545 Combine like terms: -4.545454545 + 4.545454545 = 0.000000000 0.000000000 + 0.8181818182x + x2 = 0 + 4.545454545 0.8181818182x + x2 = 0 + 4.545454545 Combine like terms: 0 + 4.545454545 = 4.545454545 0.8181818182x + x2 = 4.545454545 The x term is 0.8181818182x. Take half its coefficient (0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. 0.8181818182x + 0.1673553719 + x2 = 4.545454545 + 0.1673553719 Reorder the terms: 0.1673553719 + 0.8181818182x + x2 = 4.545454545 + 0.1673553719 Combine like terms: 4.545454545 + 0.1673553719 = 4.7128099169 0.1673553719 + 0.8181818182x + x2 = 4.7128099169 Factor a perfect square on the left side: (x + 0.4090909091)(x + 0.4090909091) = 4.7128099169 Calculate the square root of the right side: 2.170900716 Break this problem into two subproblems by setting (x + 0.4090909091) equal to 2.170900716 and -2.170900716.Subproblem 1
x + 0.4090909091 = 2.170900716 Simplifying x + 0.4090909091 = 2.170900716 Reorder the terms: 0.4090909091 + x = 2.170900716 Solving 0.4090909091 + x = 2.170900716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + x = 2.170900716 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + x = 2.170900716 + -0.4090909091 x = 2.170900716 + -0.4090909091 Combine like terms: 2.170900716 + -0.4090909091 = 1.7618098069 x = 1.7618098069 Simplifying x = 1.7618098069Subproblem 2
x + 0.4090909091 = -2.170900716 Simplifying x + 0.4090909091 = -2.170900716 Reorder the terms: 0.4090909091 + x = -2.170900716 Solving 0.4090909091 + x = -2.170900716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + x = -2.170900716 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + x = -2.170900716 + -0.4090909091 x = -2.170900716 + -0.4090909091 Combine like terms: -2.170900716 + -0.4090909091 = -2.5799916251 x = -2.5799916251 Simplifying x = -2.5799916251Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7618098069, -2.5799916251}Solution
x = {1.7618098069, -2.5799916251}
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