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Simplifying 2 + -3x(3x + 5) = 0 Reorder the terms: 2 + -3x(5 + 3x) = 0 2 + (5 * -3x + 3x * -3x) = 0 2 + (-15x + -9x2) = 0 Solving 2 + -15x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.2222222222 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 1.666666667x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 1.666666667x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + 0.2222222222 1.666666667x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 1.666666667x + x2 = 0.2222222222 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 0.2222222222 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 0.2222222222 + 0.6944444447 Combine like terms: 0.2222222222 + 0.6944444447 = 0.9166666669 0.6944444447 + 1.666666667x + x2 = 0.9166666669 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 0.9166666669 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 0.957427108 and -0.957427108.Subproblem 1
x + 0.8333333335 = 0.957427108 Simplifying x + 0.8333333335 = 0.957427108 Reorder the terms: 0.8333333335 + x = 0.957427108 Solving 0.8333333335 + x = 0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 0.957427108 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 0.957427108 + -0.8333333335 x = 0.957427108 + -0.8333333335 Combine like terms: 0.957427108 + -0.8333333335 = 0.1240937745 x = 0.1240937745 Simplifying x = 0.1240937745Subproblem 2
x + 0.8333333335 = -0.957427108 Simplifying x + 0.8333333335 = -0.957427108 Reorder the terms: 0.8333333335 + x = -0.957427108 Solving 0.8333333335 + x = -0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -0.957427108 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -0.957427108 + -0.8333333335 x = -0.957427108 + -0.8333333335 Combine like terms: -0.957427108 + -0.8333333335 = -1.7907604415 x = -1.7907604415 Simplifying x = -1.7907604415Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1240937745, -1.7907604415}
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