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Simplifying 12x2 + -10x + 10 = 0 Reorder the terms: 10 + -10x + 12x2 = 0 Solving 10 + -10x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -5x + 6x2) = 0 Ignore the factor 2.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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