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Simplifying 2x + -1(x + 5) = 6x(x + 1) Reorder the terms: 2x + -1(5 + x) = 6x(x + 1) 2x + (5 * -1 + x * -1) = 6x(x + 1) 2x + (-5 + -1x) = 6x(x + 1) Reorder the terms: -5 + 2x + -1x = 6x(x + 1) Combine like terms: 2x + -1x = 1x -5 + 1x = 6x(x + 1) Reorder the terms: -5 + 1x = 6x(1 + x) -5 + 1x = (1 * 6x + x * 6x) -5 + 1x = (6x + 6x2) Solving -5 + 1x = 6x + 6x2 Solving for variable 'x'. Combine like terms: 1x + -6x = -5x -5 + -5x + -6x2 = 6x + 6x2 + -6x + -6x2 Reorder the terms: -5 + -5x + -6x2 = 6x + -6x + 6x2 + -6x2 Combine like terms: 6x + -6x = 0 -5 + -5x + -6x2 = 0 + 6x2 + -6x2 -5 + -5x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -5 + -5x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 5x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying 5 + 5x + 6x2 = 0 Solving 5 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 0.8333333333x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 0.8333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 0.8333333333x + x2 = 0 + -0.8333333333 0.8333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 0.8333333333x + x2 = -0.8333333333 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 = -0.8333333333 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = -0.8333333333 + 0.1736111111 Combine like terms: -0.8333333333 + 0.1736111111 = -0.6597222222 0.1736111111 + 0.8333333333x + x2 = -0.6597222222 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = -0.6597222222 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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