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Simplifying 36x2 + 6x + -8 = 0 Reorder the terms: -8 + 6x + 36x2 = 0 Solving -8 + 6x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 3x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 3x + 18x2)' equal to zero and attempt to solve: Simplifying -4 + 3x + 18x2 = 0 Solving -4 + 3x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2222222222 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.1666666667x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 0.1666666667x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 0.1666666667x + x2 = 0 + 0.2222222222 0.1666666667x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 0.1666666667x + x2 = 0.2222222222 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 0.2222222222 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 0.2222222222 + 0.006944444447 Combine like terms: 0.2222222222 + 0.006944444447 = 0.229166666647 0.006944444447 + 0.1666666667x + x2 = 0.229166666647 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 0.229166666647 Calculate the square root of the right side: 0.478713554 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 0.478713554 and -0.478713554.Subproblem 1
x + 0.08333333335 = 0.478713554 Simplifying x + 0.08333333335 = 0.478713554 Reorder the terms: 0.08333333335 + x = 0.478713554 Solving 0.08333333335 + x = 0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 0.478713554 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 0.478713554 + -0.08333333335 x = 0.478713554 + -0.08333333335 Combine like terms: 0.478713554 + -0.08333333335 = 0.39538022065 x = 0.39538022065 Simplifying x = 0.39538022065Subproblem 2
x + 0.08333333335 = -0.478713554 Simplifying x + 0.08333333335 = -0.478713554 Reorder the terms: 0.08333333335 + x = -0.478713554 Solving 0.08333333335 + x = -0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -0.478713554 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -0.478713554 + -0.08333333335 x = -0.478713554 + -0.08333333335 Combine like terms: -0.478713554 + -0.08333333335 = -0.56204688735 x = -0.56204688735 Simplifying x = -0.56204688735Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.39538022065, -0.56204688735}Solution
x = {0.39538022065, -0.56204688735}
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