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Simplifying [(27h)(27h)] + -72h + 48 = 0 Remove parenthesis around (27h) [27h(27h)] + -72h + 48 = 0 Remove parenthesis around (27h) [27h * 27h] + -72h + 48 = 0 Reorder the terms for easier multiplication: [27 * 27h * h] + -72h + 48 = 0 Multiply 27 * 27 [729h * h] + -72h + 48 = 0 Multiply h * h [729h2] + -72h + 48 = 0 Reorder the terms: 48 + -72h + [729h2] = 0 Solving 48 + -72h + [729h2] = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3'. 3(16 + -24h + [243h2]) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(16 + -24h + [243h2])' equal to zero and attempt to solve: Simplifying 16 + -24h + [243h2] = 0 Solving 16 + -24h + [243h2] = 0 Begin completing the square. Divide all terms by 243 the coefficient of the squared term: Divide each side by '243'. 0.0658436214 + -0.0987654321h + h2 = 0 Move the constant term to the right: Add '-0.0658436214' to each side of the equation. 0.0658436214 + -0.0987654321h + -0.0658436214 + h2 = 0 + -0.0658436214 Reorder the terms: 0.0658436214 + -0.0658436214 + -0.0987654321h + h2 = 0 + -0.0658436214 Combine like terms: 0.0658436214 + -0.0658436214 = 0.0000000000 0.0000000000 + -0.0987654321h + h2 = 0 + -0.0658436214 -0.0987654321h + h2 = 0 + -0.0658436214 Combine like terms: 0 + -0.0658436214 = -0.0658436214 -0.0987654321h + h2 = -0.0658436214 The h term is -0.0987654321h. Take half its coefficient (-0.04938271605). Square it (0.002438652644) and add it to both sides. Add '0.002438652644' to each side of the equation. -0.0987654321h + 0.002438652644 + h2 = -0.0658436214 + 0.002438652644 Reorder the terms: 0.002438652644 + -0.0987654321h + h2 = -0.0658436214 + 0.002438652644 Combine like terms: -0.0658436214 + 0.002438652644 = -0.063404968756 0.002438652644 + -0.0987654321h + h2 = -0.063404968756 Factor a perfect square on the left side: ([h] + -0.04938271605)([h] + -0.04938271605) = -0.063404968756 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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