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Simplifying 190x2 + 55x + 140 = 0 Reorder the terms: 140 + 55x + 190x2 = 0 Solving 140 + 55x + 190x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(28 + 11x + 38x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(28 + 11x + 38x2)' equal to zero and attempt to solve: Simplifying 28 + 11x + 38x2 = 0 Solving 28 + 11x + 38x2 = 0 Begin completing the square. Divide all terms by 38 the coefficient of the squared term: Divide each side by '38'. 0.7368421053 + 0.2894736842x + x2 = 0 Move the constant term to the right: Add '-0.7368421053' to each side of the equation. 0.7368421053 + 0.2894736842x + -0.7368421053 + x2 = 0 + -0.7368421053 Reorder the terms: 0.7368421053 + -0.7368421053 + 0.2894736842x + x2 = 0 + -0.7368421053 Combine like terms: 0.7368421053 + -0.7368421053 = 0.0000000000 0.0000000000 + 0.2894736842x + x2 = 0 + -0.7368421053 0.2894736842x + x2 = 0 + -0.7368421053 Combine like terms: 0 + -0.7368421053 = -0.7368421053 0.2894736842x + x2 = -0.7368421053 The x term is 0.2894736842x. Take half its coefficient (0.1447368421). Square it (0.02094875346) and add it to both sides. Add '0.02094875346' to each side of the equation. 0.2894736842x + 0.02094875346 + x2 = -0.7368421053 + 0.02094875346 Reorder the terms: 0.02094875346 + 0.2894736842x + x2 = -0.7368421053 + 0.02094875346 Combine like terms: -0.7368421053 + 0.02094875346 = -0.71589335184 0.02094875346 + 0.2894736842x + x2 = -0.71589335184 Factor a perfect square on the left side: (x + 0.1447368421)(x + 0.1447368421) = -0.71589335184 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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