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Simplifying 150x2 + 110x + 26 = 0 Reorder the terms: 26 + 110x + 150x2 = 0 Solving 26 + 110x + 150x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(13 + 55x + 75x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + 55x + 75x2)' equal to zero and attempt to solve: Simplifying 13 + 55x + 75x2 = 0 Solving 13 + 55x + 75x2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. 0.1733333333 + 0.7333333333x + x2 = 0 Move the constant term to the right: Add '-0.1733333333' to each side of the equation. 0.1733333333 + 0.7333333333x + -0.1733333333 + x2 = 0 + -0.1733333333 Reorder the terms: 0.1733333333 + -0.1733333333 + 0.7333333333x + x2 = 0 + -0.1733333333 Combine like terms: 0.1733333333 + -0.1733333333 = 0.0000000000 0.0000000000 + 0.7333333333x + x2 = 0 + -0.1733333333 0.7333333333x + x2 = 0 + -0.1733333333 Combine like terms: 0 + -0.1733333333 = -0.1733333333 0.7333333333x + x2 = -0.1733333333 The x term is 0.7333333333x. Take half its coefficient (0.3666666667). Square it (0.1344444445) and add it to both sides. Add '0.1344444445' to each side of the equation. 0.7333333333x + 0.1344444445 + x2 = -0.1733333333 + 0.1344444445 Reorder the terms: 0.1344444445 + 0.7333333333x + x2 = -0.1733333333 + 0.1344444445 Combine like terms: -0.1733333333 + 0.1344444445 = -0.0388888888 0.1344444445 + 0.7333333333x + x2 = -0.0388888888 Factor a perfect square on the left side: (x + 0.3666666667)(x + 0.3666666667) = -0.0388888888 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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