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Simplifying -45v + 9v2 + -63v3 = 0 Solving -45v + 9v2 + -63v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '9v'. 9v(-5 + v + -7v2) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(-5 + v + -7v2)' equal to zero and attempt to solve: Simplifying -5 + v + -7v2 = 0 Solving -5 + v + -7v2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 0.7142857143 + -0.1428571429v + v2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -0.1428571429v + -0.7142857143 + v2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -0.1428571429v + v2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -0.1428571429v + v2 = 0 + -0.7142857143 -0.1428571429v + v2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -0.1428571429v + v2 = -0.7142857143 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1428571429v + 0.25 + v2 = -0.7142857143 + 0.25 Reorder the terms: 0.25 + -0.1428571429v + v2 = -0.7142857143 + 0.25 Combine like terms: -0.7142857143 + 0.25 = -0.4642857143 0.25 + -0.1428571429v + v2 = -0.4642857143 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = -0.4642857143 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.Solution
v = {0}
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