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Simplifying 9x2 + 2x = 83 Reorder the terms: 2x + 9x2 = 83 Solving 2x + 9x2 = 83 Solving for variable 'x'. Reorder the terms: -83 + 2x + 9x2 = 83 + -83 Combine like terms: 83 + -83 = 0 -83 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -9.222222222 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '9.222222222' to each side of the equation. -9.222222222 + 0.2222222222x + 9.222222222 + x2 = 0 + 9.222222222 Reorder the terms: -9.222222222 + 9.222222222 + 0.2222222222x + x2 = 0 + 9.222222222 Combine like terms: -9.222222222 + 9.222222222 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + 9.222222222 0.2222222222x + x2 = 0 + 9.222222222 Combine like terms: 0 + 9.222222222 = 9.222222222 0.2222222222x + x2 = 9.222222222 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 = 9.222222222 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 9.222222222 + 0.01234567901 Combine like terms: 9.222222222 + 0.01234567901 = 9.23456790101 0.01234567901 + 0.2222222222x + x2 = 9.23456790101 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 9.23456790101 Calculate the square root of the right side: 3.038843185 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 3.038843185 and -3.038843185.Subproblem 1
x + 0.1111111111 = 3.038843185 Simplifying x + 0.1111111111 = 3.038843185 Reorder the terms: 0.1111111111 + x = 3.038843185 Solving 0.1111111111 + x = 3.038843185 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 = 3.038843185 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 3.038843185 + -0.1111111111 x = 3.038843185 + -0.1111111111 Combine like terms: 3.038843185 + -0.1111111111 = 2.9277320739 x = 2.9277320739 Simplifying x = 2.9277320739Subproblem 2
x + 0.1111111111 = -3.038843185 Simplifying x + 0.1111111111 = -3.038843185 Reorder the terms: 0.1111111111 + x = -3.038843185 Solving 0.1111111111 + x = -3.038843185 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 = -3.038843185 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -3.038843185 + -0.1111111111 x = -3.038843185 + -0.1111111111 Combine like terms: -3.038843185 + -0.1111111111 = -3.1499542961 x = -3.1499542961 Simplifying x = -3.1499542961Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9277320739, -3.1499542961}
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