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Simplifying 6(-6x + -5) * 6x + -5 = 245 Reorder the terms: 6(-5 + -6x) * 6x + -5 = 245 Reorder the terms for easier multiplication: 6 * 6x(-5 + -6x) + -5 = 245 Multiply 6 * 6 36x(-5 + -6x) + -5 = 245 (-5 * 36x + -6x * 36x) + -5 = 245 (-180x + -216x2) + -5 = 245 Reorder the terms: -5 + -180x + -216x2 = 245 Solving -5 + -180x + -216x2 = 245 Solving for variable 'x'. Reorder the terms: -5 + -245 + -180x + -216x2 = 245 + -245 Combine like terms: -5 + -245 = -250 -250 + -180x + -216x2 = 245 + -245 Combine like terms: 245 + -245 = 0 -250 + -180x + -216x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(125 + 90x + 108x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(125 + 90x + 108x2)' equal to zero and attempt to solve: Simplifying 125 + 90x + 108x2 = 0 Solving 125 + 90x + 108x2 = 0 Begin completing the square. Divide all terms by 108 the coefficient of the squared term: Divide each side by '108'. 1.157407407 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '-1.157407407' to each side of the equation. 1.157407407 + 0.8333333333x + -1.157407407 + x2 = 0 + -1.157407407 Reorder the terms: 1.157407407 + -1.157407407 + 0.8333333333x + x2 = 0 + -1.157407407 Combine like terms: 1.157407407 + -1.157407407 = 0.000000000 0.000000000 + 0.8333333333x + x2 = 0 + -1.157407407 0.8333333333x + x2 = 0 + -1.157407407 Combine like terms: 0 + -1.157407407 = -1.157407407 0.8333333333x + x2 = -1.157407407 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = -1.157407407 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = -1.157407407 + 0.1736111111 Combine like terms: -1.157407407 + 0.1736111111 = -0.9837962959 0.1736111111 + 0.8333333333x + x2 = -0.9837962959 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = -0.9837962959 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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