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Simplifying 3x(3x) + 10x + -8 = 0 Remove parenthesis around (3x) 3x * 3x + 10x + -8 = 0 Reorder the terms for easier multiplication: 3 * 3x * x + 10x + -8 = 0 Multiply 3 * 3 9x * x + 10x + -8 = 0 Multiply x * x 9x2 + 10x + -8 = 0 Reorder the terms: -8 + 10x + 9x2 = 0 Solving -8 + 10x + 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'. -0.8888888889 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 1.111111111x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 1.111111111x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 1.111111111x + x2 = 0 + 0.8888888889 1.111111111x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 1.111111111x + x2 = 0.8888888889 The x term is 1.111111111x. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111x + 0.3086419752 + x2 = 0.8888888889 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = 0.8888888889 + 0.3086419752 Combine like terms: 0.8888888889 + 0.3086419752 = 1.1975308641 0.3086419752 + 1.111111111x + x2 = 1.1975308641 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 1.1975308641 Calculate the square root of the right side: 1.094317533 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 1.094317533 and -1.094317533.Subproblem 1
x + 0.5555555555 = 1.094317533 Simplifying x + 0.5555555555 = 1.094317533 Reorder the terms: 0.5555555555 + x = 1.094317533 Solving 0.5555555555 + x = 1.094317533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 1.094317533 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 1.094317533 + -0.5555555555 x = 1.094317533 + -0.5555555555 Combine like terms: 1.094317533 + -0.5555555555 = 0.5387619775 x = 0.5387619775 Simplifying x = 0.5387619775Subproblem 2
x + 0.5555555555 = -1.094317533 Simplifying x + 0.5555555555 = -1.094317533 Reorder the terms: 0.5555555555 + x = -1.094317533 Solving 0.5555555555 + x = -1.094317533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -1.094317533 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -1.094317533 + -0.5555555555 x = -1.094317533 + -0.5555555555 Combine like terms: -1.094317533 + -0.5555555555 = -1.6498730885 x = -1.6498730885 Simplifying x = -1.6498730885Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5387619775, -1.6498730885}
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