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Simplifying 4h2 + -52h + -144 = 0 Reorder the terms: -144 + -52h + 4h2 = 0 Solving -144 + -52h + 4h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '4'. 4(-36 + -13h + h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-36 + -13h + h2)' equal to zero and attempt to solve: Simplifying -36 + -13h + h2 = 0 Solving -36 + -13h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -13h + 36 + h2 = 0 + 36 Reorder the terms: -36 + 36 + -13h + h2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -13h + h2 = 0 + 36 -13h + h2 = 0 + 36 Combine like terms: 0 + 36 = 36 -13h + h2 = 36 The h term is -13h. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13h + 42.25 + h2 = 36 + 42.25 Reorder the terms: 42.25 + -13h + h2 = 36 + 42.25 Combine like terms: 36 + 42.25 = 78.25 42.25 + -13h + h2 = 78.25 Factor a perfect square on the left side: (h + -6.5)(h + -6.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (h + -6.5) equal to 8.845903006 and -8.845903006.Subproblem 1
h + -6.5 = 8.845903006 Simplifying h + -6.5 = 8.845903006 Reorder the terms: -6.5 + h = 8.845903006 Solving -6.5 + h = 8.845903006 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + h = 8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + h = 8.845903006 + 6.5 h = 8.845903006 + 6.5 Combine like terms: 8.845903006 + 6.5 = 15.345903006 h = 15.345903006 Simplifying h = 15.345903006Subproblem 2
h + -6.5 = -8.845903006 Simplifying h + -6.5 = -8.845903006 Reorder the terms: -6.5 + h = -8.845903006 Solving -6.5 + h = -8.845903006 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + h = -8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + h = -8.845903006 + 6.5 h = -8.845903006 + 6.5 Combine like terms: -8.845903006 + 6.5 = -2.345903006 h = -2.345903006 Simplifying h = -2.345903006Solution
The solution to the problem is based on the solutions from the subproblems. h = {15.345903006, -2.345903006}Solution
h = {15.345903006, -2.345903006}
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