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Simplifying 18x2 + 5x + -72 = 0 Reorder the terms: -72 + 5x + 18x2 = 0 Solving -72 + 5x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -4 + 0.2777777778x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.2777777778x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.2777777778x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.2777777778x + x2 = 0 + 4 0.2777777778x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.2777777778x + x2 = 4 The x term is 0.2777777778x. Take half its coefficient (0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. 0.2777777778x + 0.01929012346 + x2 = 4 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778x + x2 = 4 + 0.01929012346 Combine like terms: 4 + 0.01929012346 = 4.01929012346 0.01929012346 + 0.2777777778x + x2 = 4.01929012346 Factor a perfect square on the left side: (x + 0.1388888889)(x + 0.1388888889) = 4.01929012346 Calculate the square root of the right side: 2.004816731 Break this problem into two subproblems by setting (x + 0.1388888889) equal to 2.004816731 and -2.004816731.Subproblem 1
x + 0.1388888889 = 2.004816731 Simplifying x + 0.1388888889 = 2.004816731 Reorder the terms: 0.1388888889 + x = 2.004816731 Solving 0.1388888889 + x = 2.004816731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + x = 2.004816731 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = 2.004816731 + -0.1388888889 x = 2.004816731 + -0.1388888889 Combine like terms: 2.004816731 + -0.1388888889 = 1.8659278421 x = 1.8659278421 Simplifying x = 1.8659278421Subproblem 2
x + 0.1388888889 = -2.004816731 Simplifying x + 0.1388888889 = -2.004816731 Reorder the terms: 0.1388888889 + x = -2.004816731 Solving 0.1388888889 + x = -2.004816731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + x = -2.004816731 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = -2.004816731 + -0.1388888889 x = -2.004816731 + -0.1388888889 Combine like terms: -2.004816731 + -0.1388888889 = -2.1437056199 x = -2.1437056199 Simplifying x = -2.1437056199Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8659278421, -2.1437056199}
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