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Simplifying 9x2 + -2x + -90 = 0 Reorder the terms: -90 + -2x + 9x2 = 0 Solving -90 + -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'. -10 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.2222222222x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -0.2222222222x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.2222222222x + x2 = 0 + 10 -0.2222222222x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.2222222222x + x2 = 10 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 = 10 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 10 + 0.01234567901 Combine like terms: 10 + 0.01234567901 = 10.01234567901 0.01234567901 + -0.2222222222x + x2 = 10.01234567901 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 10.01234567901 Calculate the square root of the right side: 3.164229081 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 3.164229081 and -3.164229081.Subproblem 1
x + -0.1111111111 = 3.164229081 Simplifying x + -0.1111111111 = 3.164229081 Reorder the terms: -0.1111111111 + x = 3.164229081 Solving -0.1111111111 + x = 3.164229081 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 = 3.164229081 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 3.164229081 + 0.1111111111 x = 3.164229081 + 0.1111111111 Combine like terms: 3.164229081 + 0.1111111111 = 3.2753401921 x = 3.2753401921 Simplifying x = 3.2753401921Subproblem 2
x + -0.1111111111 = -3.164229081 Simplifying x + -0.1111111111 = -3.164229081 Reorder the terms: -0.1111111111 + x = -3.164229081 Solving -0.1111111111 + x = -3.164229081 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 = -3.164229081 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -3.164229081 + 0.1111111111 x = -3.164229081 + 0.1111111111 Combine like terms: -3.164229081 + 0.1111111111 = -3.0531179699 x = -3.0531179699 Simplifying x = -3.0531179699Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2753401921, -3.0531179699}
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