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Simplifying 9x2 + 2x + -2 = 22 Reorder the terms: -2 + 2x + 9x2 = 22 Solving -2 + 2x + 9x2 = 22 Solving for variable 'x'. Reorder the terms: -2 + -22 + 2x + 9x2 = 22 + -22 Combine like terms: -2 + -22 = -24 -24 + 2x + 9x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -24 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.666666667 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 0.2222222222x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 0.2222222222x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + 2.666666667 0.2222222222x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 0.2222222222x + x2 = 2.666666667 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 = 2.666666667 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 2.666666667 + 0.01234567901 Combine like terms: 2.666666667 + 0.01234567901 = 2.67901234601 0.01234567901 + 0.2222222222x + x2 = 2.67901234601 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 2.67901234601 Calculate the square root of the right side: 1.636768874 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 1.636768874 and -1.636768874.Subproblem 1
x + 0.1111111111 = 1.636768874 Simplifying x + 0.1111111111 = 1.636768874 Reorder the terms: 0.1111111111 + x = 1.636768874 Solving 0.1111111111 + x = 1.636768874 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 = 1.636768874 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.636768874 + -0.1111111111 x = 1.636768874 + -0.1111111111 Combine like terms: 1.636768874 + -0.1111111111 = 1.5256577629 x = 1.5256577629 Simplifying x = 1.5256577629Subproblem 2
x + 0.1111111111 = -1.636768874 Simplifying x + 0.1111111111 = -1.636768874 Reorder the terms: 0.1111111111 + x = -1.636768874 Solving 0.1111111111 + x = -1.636768874 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 = -1.636768874 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.636768874 + -0.1111111111 x = -1.636768874 + -0.1111111111 Combine like terms: -1.636768874 + -0.1111111111 = -1.7478799851 x = -1.7478799851 Simplifying x = -1.7478799851Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5256577629, -1.7478799851}
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