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Simplifying -30x = 9x2 + -2 Reorder the terms: -30x = -2 + 9x2 Solving -30x = -2 + 9x2 Solving for variable 'x'. Reorder the terms: 2 + -30x + -9x2 = -2 + 9x2 + 2 + -9x2 Reorder the terms: 2 + -30x + -9x2 = -2 + 2 + 9x2 + -9x2 Combine like terms: -2 + 2 = 0 2 + -30x + -9x2 = 0 + 9x2 + -9x2 2 + -30x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 2 + -30x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.2222222222 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 3.333333333x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 3.333333333x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 3.333333333x + x2 = 0 + 0.2222222222 3.333333333x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 3.333333333x + x2 = 0.2222222222 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 = 0.2222222222 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 0.2222222222 + 2.777777779 Combine like terms: 0.2222222222 + 2.777777779 = 3.0000000012 2.777777779 + 3.333333333x + x2 = 3.0000000012 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 3.0000000012 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 1.666666667) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 1.666666667 = 1.732050808 Simplifying x + 1.666666667 = 1.732050808 Reorder the terms: 1.666666667 + x = 1.732050808 Solving 1.666666667 + x = 1.732050808 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 = 1.732050808 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 1.732050808 + -1.666666667 x = 1.732050808 + -1.666666667 Combine like terms: 1.732050808 + -1.666666667 = 0.065384141 x = 0.065384141 Simplifying x = 0.065384141Subproblem 2
x + 1.666666667 = -1.732050808 Simplifying x + 1.666666667 = -1.732050808 Reorder the terms: 1.666666667 + x = -1.732050808 Solving 1.666666667 + x = -1.732050808 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 = -1.732050808 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -1.732050808 + -1.666666667 x = -1.732050808 + -1.666666667 Combine like terms: -1.732050808 + -1.666666667 = -3.398717475 x = -3.398717475 Simplifying x = -3.398717475Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.065384141, -3.398717475}
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