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Simplifying -10 + 6x + 36x2 = 0 Solving -10 + 6x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 3x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 3x + 18x2)' equal to zero and attempt to solve: Simplifying -5 + 3x + 18x2 = 0 Solving -5 + 3x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2777777778 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.1666666667x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + 0.1666666667x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + 0.1666666667x + x2 = 0 + 0.2777777778 0.1666666667x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 0.1666666667x + x2 = 0.2777777778 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 = 0.2777777778 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 0.2777777778 + 0.006944444447 Combine like terms: 0.2777777778 + 0.006944444447 = 0.284722222247 0.006944444447 + 0.1666666667x + x2 = 0.284722222247 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 0.284722222247 Calculate the square root of the right side: 0.533593686 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 0.533593686 and -0.533593686.Subproblem 1
x + 0.08333333335 = 0.533593686 Simplifying x + 0.08333333335 = 0.533593686 Reorder the terms: 0.08333333335 + x = 0.533593686 Solving 0.08333333335 + x = 0.533593686 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 = 0.533593686 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 0.533593686 + -0.08333333335 x = 0.533593686 + -0.08333333335 Combine like terms: 0.533593686 + -0.08333333335 = 0.45026035265 x = 0.45026035265 Simplifying x = 0.45026035265Subproblem 2
x + 0.08333333335 = -0.533593686 Simplifying x + 0.08333333335 = -0.533593686 Reorder the terms: 0.08333333335 + x = -0.533593686 Solving 0.08333333335 + x = -0.533593686 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 = -0.533593686 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -0.533593686 + -0.08333333335 x = -0.533593686 + -0.08333333335 Combine like terms: -0.533593686 + -0.08333333335 = -0.61692701935 x = -0.61692701935 Simplifying x = -0.61692701935Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.45026035265, -0.61692701935}Solution
x = {0.45026035265, -0.61692701935}
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