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Simplifying 6x(6x) + 4x = -10 Remove parenthesis around (6x) 6x * 6x + 4x = -10 Reorder the terms for easier multiplication: 6 * 6x * x + 4x = -10 Multiply 6 * 6 36x * x + 4x = -10 Multiply x * x 36x2 + 4x = -10 Reorder the terms: 4x + 36x2 = -10 Solving 4x + 36x2 = -10 Solving for variable 'x'. Reorder the terms: 10 + 4x + 36x2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + 4x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 2x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 2x + 18x2)' equal to zero and attempt to solve: Simplifying 5 + 2x + 18x2 = 0 Solving 5 + 2x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2777777778 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '-0.2777777778' to each side of the equation. 0.2777777778 + 0.1111111111x + -0.2777777778 + x2 = 0 + -0.2777777778 Reorder the terms: 0.2777777778 + -0.2777777778 + 0.1111111111x + x2 = 0 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + 0.1111111111x + x2 = 0 + -0.2777777778 0.1111111111x + x2 = 0 + -0.2777777778 Combine like terms: 0 + -0.2777777778 = -0.2777777778 0.1111111111x + x2 = -0.2777777778 The x term is 0.1111111111x. Take half its coefficient (0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. 0.1111111111x + 0.003086419752 + x2 = -0.2777777778 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = -0.2777777778 + 0.003086419752 Combine like terms: -0.2777777778 + 0.003086419752 = -0.274691358048 0.003086419752 + 0.1111111111x + x2 = -0.274691358048 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = -0.274691358048 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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