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Simplifying 18x2 + 6x + -8 = 0 Reorder the terms: -8 + 6x + 18x2 = 0 Solving -8 + 6x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 3x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 3x + 9x2)' equal to zero and attempt to solve: Simplifying -4 + 3x + 9x2 = 0 Solving -4 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 0.3333333333x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 0.3333333333x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.4444444444 0.3333333333x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 0.3333333333x + x2 = 0.4444444444 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.4444444444 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.4444444444 + 0.02777777779 Combine like terms: 0.4444444444 + 0.02777777779 = 0.47222222219 0.02777777779 + 0.3333333333x + x2 = 0.47222222219 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.47222222219 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.687184271 and -0.687184271.Subproblem 1
x + 0.1666666667 = 0.687184271 Simplifying x + 0.1666666667 = 0.687184271 Reorder the terms: 0.1666666667 + x = 0.687184271 Solving 0.1666666667 + x = 0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.687184271 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.687184271 + -0.1666666667 x = 0.687184271 + -0.1666666667 Combine like terms: 0.687184271 + -0.1666666667 = 0.5205176043 x = 0.5205176043 Simplifying x = 0.5205176043Subproblem 2
x + 0.1666666667 = -0.687184271 Simplifying x + 0.1666666667 = -0.687184271 Reorder the terms: 0.1666666667 + x = -0.687184271 Solving 0.1666666667 + x = -0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.687184271 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.687184271 + -0.1666666667 x = -0.687184271 + -0.1666666667 Combine like terms: -0.687184271 + -0.1666666667 = -0.8538509377 x = -0.8538509377 Simplifying x = -0.8538509377Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5205176043, -0.8538509377}Solution
x = {0.5205176043, -0.8538509377}
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