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Simplifying 44x2 + 14x + -238 = 0 Reorder the terms: -238 + 14x + 44x2 = 0 Solving -238 + 14x + 44x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-119 + 7x + 22x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-119 + 7x + 22x2)' equal to zero and attempt to solve: Simplifying -119 + 7x + 22x2 = 0 Solving -119 + 7x + 22x2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -5.409090909 + 0.3181818182x + x2 = 0 Move the constant term to the right: Add '5.409090909' to each side of the equation. -5.409090909 + 0.3181818182x + 5.409090909 + x2 = 0 + 5.409090909 Reorder the terms: -5.409090909 + 5.409090909 + 0.3181818182x + x2 = 0 + 5.409090909 Combine like terms: -5.409090909 + 5.409090909 = 0.000000000 0.000000000 + 0.3181818182x + x2 = 0 + 5.409090909 0.3181818182x + x2 = 0 + 5.409090909 Combine like terms: 0 + 5.409090909 = 5.409090909 0.3181818182x + x2 = 5.409090909 The x term is 0.3181818182x. Take half its coefficient (0.1590909091). Square it (0.02530991736) and add it to both sides. Add '0.02530991736' to each side of the equation. 0.3181818182x + 0.02530991736 + x2 = 5.409090909 + 0.02530991736 Reorder the terms: 0.02530991736 + 0.3181818182x + x2 = 5.409090909 + 0.02530991736 Combine like terms: 5.409090909 + 0.02530991736 = 5.43440082636 0.02530991736 + 0.3181818182x + x2 = 5.43440082636 Factor a perfect square on the left side: (x + 0.1590909091)(x + 0.1590909091) = 5.43440082636 Calculate the square root of the right side: 2.331180136 Break this problem into two subproblems by setting (x + 0.1590909091) equal to 2.331180136 and -2.331180136.Subproblem 1
x + 0.1590909091 = 2.331180136 Simplifying x + 0.1590909091 = 2.331180136 Reorder the terms: 0.1590909091 + x = 2.331180136 Solving 0.1590909091 + x = 2.331180136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1590909091' to each side of the equation. 0.1590909091 + -0.1590909091 + x = 2.331180136 + -0.1590909091 Combine like terms: 0.1590909091 + -0.1590909091 = 0.0000000000 0.0000000000 + x = 2.331180136 + -0.1590909091 x = 2.331180136 + -0.1590909091 Combine like terms: 2.331180136 + -0.1590909091 = 2.1720892269 x = 2.1720892269 Simplifying x = 2.1720892269Subproblem 2
x + 0.1590909091 = -2.331180136 Simplifying x + 0.1590909091 = -2.331180136 Reorder the terms: 0.1590909091 + x = -2.331180136 Solving 0.1590909091 + x = -2.331180136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1590909091' to each side of the equation. 0.1590909091 + -0.1590909091 + x = -2.331180136 + -0.1590909091 Combine like terms: 0.1590909091 + -0.1590909091 = 0.0000000000 0.0000000000 + x = -2.331180136 + -0.1590909091 x = -2.331180136 + -0.1590909091 Combine like terms: -2.331180136 + -0.1590909091 = -2.4902710451 x = -2.4902710451 Simplifying x = -2.4902710451Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1720892269, -2.4902710451}Solution
x = {2.1720892269, -2.4902710451}
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