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Simplifying 9x2 + 2x + -12 = 0 Reorder the terms: -12 + 2x + 9x2 = 0 Solving -12 + 2x + 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'. -1.333333333 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 0.2222222222x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 0.2222222222x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + 1.333333333 0.2222222222x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 0.2222222222x + x2 = 1.333333333 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 1.333333333 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 1.333333333 + 0.01234567901 Combine like terms: 1.333333333 + 0.01234567901 = 1.34567901201 0.01234567901 + 0.2222222222x + x2 = 1.34567901201 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 1.34567901201 Calculate the square root of the right side: 1.160034056 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 1.160034056 and -1.160034056.Subproblem 1
x + 0.1111111111 = 1.160034056 Simplifying x + 0.1111111111 = 1.160034056 Reorder the terms: 0.1111111111 + x = 1.160034056 Solving 0.1111111111 + x = 1.160034056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 1.160034056 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.160034056 + -0.1111111111 x = 1.160034056 + -0.1111111111 Combine like terms: 1.160034056 + -0.1111111111 = 1.0489229449 x = 1.0489229449 Simplifying x = 1.0489229449Subproblem 2
x + 0.1111111111 = -1.160034056 Simplifying x + 0.1111111111 = -1.160034056 Reorder the terms: 0.1111111111 + x = -1.160034056 Solving 0.1111111111 + x = -1.160034056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -1.160034056 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.160034056 + -0.1111111111 x = -1.160034056 + -0.1111111111 Combine like terms: -1.160034056 + -0.1111111111 = -1.2711451671 x = -1.2711451671 Simplifying x = -1.2711451671Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0489229449, -1.2711451671}
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