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Simplifying 36x2 + 8x + -6 = 0 Reorder the terms: -6 + 8x + 36x2 = 0 Solving -6 + 8x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 4x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 4x + 18x2)' equal to zero and attempt to solve: Simplifying -3 + 4x + 18x2 = 0 Solving -3 + 4x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.1666666667 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.2222222222x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.2222222222x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.2222222222x + x2 = 0 + 0.1666666667 0.2222222222x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 0.2222222222x + x2 = 0.1666666667 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 = 0.1666666667 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 0.1666666667 + 0.01234567901 Combine like terms: 0.1666666667 + 0.01234567901 = 0.17901234571 0.01234567901 + 0.2222222222x + x2 = 0.17901234571 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.17901234571 Calculate the square root of the right side: 0.423098506 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.423098506 and -0.423098506.Subproblem 1
x + 0.1111111111 = 0.423098506 Simplifying x + 0.1111111111 = 0.423098506 Reorder the terms: 0.1111111111 + x = 0.423098506 Solving 0.1111111111 + x = 0.423098506 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 = 0.423098506 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.423098506 + -0.1111111111 x = 0.423098506 + -0.1111111111 Combine like terms: 0.423098506 + -0.1111111111 = 0.3119873949 x = 0.3119873949 Simplifying x = 0.3119873949Subproblem 2
x + 0.1111111111 = -0.423098506 Simplifying x + 0.1111111111 = -0.423098506 Reorder the terms: 0.1111111111 + x = -0.423098506 Solving 0.1111111111 + x = -0.423098506 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 = -0.423098506 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.423098506 + -0.1111111111 x = -0.423098506 + -0.1111111111 Combine like terms: -0.423098506 + -0.1111111111 = -0.5342096171 x = -0.5342096171 Simplifying x = -0.5342096171Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3119873949, -0.5342096171}Solution
x = {0.3119873949, -0.5342096171}
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