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Simplifying (h + -7)(h + -5) = 2h + 2(h + 3) Reorder the terms: (-7 + h)(h + -5) = 2h + 2(h + 3) Reorder the terms: (-7 + h)(-5 + h) = 2h + 2(h + 3) Multiply (-7 + h) * (-5 + h) (-7(-5 + h) + h(-5 + h)) = 2h + 2(h + 3) ((-5 * -7 + h * -7) + h(-5 + h)) = 2h + 2(h + 3) ((35 + -7h) + h(-5 + h)) = 2h + 2(h + 3) (35 + -7h + (-5 * h + h * h)) = 2h + 2(h + 3) (35 + -7h + (-5h + h2)) = 2h + 2(h + 3) Combine like terms: -7h + -5h = -12h (35 + -12h + h2) = 2h + 2(h + 3) Reorder the terms: 35 + -12h + h2 = 2h + 2(3 + h) 35 + -12h + h2 = 2h + (3 * 2 + h * 2) 35 + -12h + h2 = 2h + (6 + 2h) Reorder the terms: 35 + -12h + h2 = 6 + 2h + 2h Combine like terms: 2h + 2h = 4h 35 + -12h + h2 = 6 + 4h Solving 35 + -12h + h2 = 6 + 4h Solving for variable 'h'. Reorder the terms: 35 + -6 + -12h + -4h + h2 = 6 + 4h + -6 + -4h Combine like terms: 35 + -6 = 29 29 + -12h + -4h + h2 = 6 + 4h + -6 + -4h Combine like terms: -12h + -4h = -16h 29 + -16h + h2 = 6 + 4h + -6 + -4h Reorder the terms: 29 + -16h + h2 = 6 + -6 + 4h + -4h Combine like terms: 6 + -6 = 0 29 + -16h + h2 = 0 + 4h + -4h 29 + -16h + h2 = 4h + -4h Combine like terms: 4h + -4h = 0 29 + -16h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -16h + -29 + h2 = 0 + -29 Reorder the terms: 29 + -29 + -16h + h2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -16h + h2 = 0 + -29 -16h + h2 = 0 + -29 Combine like terms: 0 + -29 = -29 -16h + h2 = -29 The h term is -16h. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16h + 64 + h2 = -29 + 64 Reorder the terms: 64 + -16h + h2 = -29 + 64 Combine like terms: -29 + 64 = 35 64 + -16h + h2 = 35 Factor a perfect square on the left side: (h + -8)(h + -8) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (h + -8) equal to 5.916079783 and -5.916079783.Subproblem 1
h + -8 = 5.916079783 Simplifying h + -8 = 5.916079783 Reorder the terms: -8 + h = 5.916079783 Solving -8 + h = 5.916079783 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + h = 5.916079783 + 8 Combine like terms: -8 + 8 = 0 0 + h = 5.916079783 + 8 h = 5.916079783 + 8 Combine like terms: 5.916079783 + 8 = 13.916079783 h = 13.916079783 Simplifying h = 13.916079783Subproblem 2
h + -8 = -5.916079783 Simplifying h + -8 = -5.916079783 Reorder the terms: -8 + h = -5.916079783 Solving -8 + h = -5.916079783 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + h = -5.916079783 + 8 Combine like terms: -8 + 8 = 0 0 + h = -5.916079783 + 8 h = -5.916079783 + 8 Combine like terms: -5.916079783 + 8 = 2.083920217 h = 2.083920217 Simplifying h = 2.083920217Solution
The solution to the problem is based on the solutions from the subproblems. h = {13.916079783, 2.083920217}
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