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Simplifying 3h2 + 24h + 564 = 0 Reorder the terms: 564 + 24h + 3h2 = 0 Solving 564 + 24h + 3h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3'. 3(188 + 8h + h2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(188 + 8h + h2)' equal to zero and attempt to solve: Simplifying 188 + 8h + h2 = 0 Solving 188 + 8h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-188' to each side of the equation. 188 + 8h + -188 + h2 = 0 + -188 Reorder the terms: 188 + -188 + 8h + h2 = 0 + -188 Combine like terms: 188 + -188 = 0 0 + 8h + h2 = 0 + -188 8h + h2 = 0 + -188 Combine like terms: 0 + -188 = -188 8h + h2 = -188 The h term is 8h. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8h + 16 + h2 = -188 + 16 Reorder the terms: 16 + 8h + h2 = -188 + 16 Combine like terms: -188 + 16 = -172 16 + 8h + h2 = -172 Factor a perfect square on the left side: (h + 4)(h + 4) = -172 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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