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Simplifying 0 = 8h2 + 24h + 560 Reorder the terms: 0 = 560 + 24h + 8h2 Solving 0 = 560 + 24h + 8h2 Solving for variable 'h'. Combine like terms: 0 + -560 = -560 -560 + -24h + -8h2 = 560 + 24h + 8h2 + -560 + -24h + -8h2 Reorder the terms: -560 + -24h + -8h2 = 560 + -560 + 24h + -24h + 8h2 + -8h2 Combine like terms: 560 + -560 = 0 -560 + -24h + -8h2 = 0 + 24h + -24h + 8h2 + -8h2 -560 + -24h + -8h2 = 24h + -24h + 8h2 + -8h2 Combine like terms: 24h + -24h = 0 -560 + -24h + -8h2 = 0 + 8h2 + -8h2 -560 + -24h + -8h2 = 8h2 + -8h2 Combine like terms: 8h2 + -8h2 = 0 -560 + -24h + -8h2 = 0 Factor out the Greatest Common Factor (GCF), '-8'. -8(70 + 3h + h2) = 0 Ignore the factor -8.Subproblem 1
Set the factor '(70 + 3h + h2)' equal to zero and attempt to solve: Simplifying 70 + 3h + h2 = 0 Solving 70 + 3h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + 3h + -70 + h2 = 0 + -70 Reorder the terms: 70 + -70 + 3h + h2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + 3h + h2 = 0 + -70 3h + h2 = 0 + -70 Combine like terms: 0 + -70 = -70 3h + h2 = -70 The h term is 3h. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3h + 2.25 + h2 = -70 + 2.25 Reorder the terms: 2.25 + 3h + h2 = -70 + 2.25 Combine like terms: -70 + 2.25 = -67.75 2.25 + 3h + h2 = -67.75 Factor a perfect square on the left side: (h + 1.5)(h + 1.5) = -67.75 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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