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Simplifying 1 + -30x + -9x2 = 0 Solving 1 + -30x + -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'. -0.1111111111 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 3.333333333x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 3.333333333x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 3.333333333x + x2 = 0 + 0.1111111111 3.333333333x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 3.333333333x + x2 = 0.1111111111 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 0.1111111111 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 0.1111111111 + 2.777777779 Combine like terms: 0.1111111111 + 2.777777779 = 2.8888888901 2.777777779 + 3.333333333x + x2 = 2.8888888901 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 2.8888888901 Calculate the square root of the right side: 1.699673172 Break this problem into two subproblems by setting (x + 1.666666667) equal to 1.699673172 and -1.699673172.Subproblem 1
x + 1.666666667 = 1.699673172 Simplifying x + 1.666666667 = 1.699673172 Reorder the terms: 1.666666667 + x = 1.699673172 Solving 1.666666667 + x = 1.699673172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 1.699673172 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 1.699673172 + -1.666666667 x = 1.699673172 + -1.666666667 Combine like terms: 1.699673172 + -1.666666667 = 0.033006505 x = 0.033006505 Simplifying x = 0.033006505Subproblem 2
x + 1.666666667 = -1.699673172 Simplifying x + 1.666666667 = -1.699673172 Reorder the terms: 1.666666667 + x = -1.699673172 Solving 1.666666667 + x = -1.699673172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -1.699673172 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -1.699673172 + -1.666666667 x = -1.699673172 + -1.666666667 Combine like terms: -1.699673172 + -1.666666667 = -3.366339839 x = -3.366339839 Simplifying x = -3.366339839Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.033006505, -3.366339839}
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