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Simplifying f2 + -8f + -7 = 0 Reorder the terms: -7 + -8f + f2 = 0 Solving -7 + -8f + f2 = 0 Solving for variable 'f'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -8f + 7 + f2 = 0 + 7 Reorder the terms: -7 + 7 + -8f + f2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8f + f2 = 0 + 7 -8f + f2 = 0 + 7 Combine like terms: 0 + 7 = 7 -8f + f2 = 7 The f term is -8f. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8f + 16 + f2 = 7 + 16 Reorder the terms: 16 + -8f + f2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + -8f + f2 = 23 Factor a perfect square on the left side: (f + -4)(f + -4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (f + -4) equal to 4.795831523 and -4.795831523.Subproblem 1
f + -4 = 4.795831523 Simplifying f + -4 = 4.795831523 Reorder the terms: -4 + f = 4.795831523 Solving -4 + f = 4.795831523 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + f = 4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + f = 4.795831523 + 4 f = 4.795831523 + 4 Combine like terms: 4.795831523 + 4 = 8.795831523 f = 8.795831523 Simplifying f = 8.795831523Subproblem 2
f + -4 = -4.795831523 Simplifying f + -4 = -4.795831523 Reorder the terms: -4 + f = -4.795831523 Solving -4 + f = -4.795831523 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + f = -4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + f = -4.795831523 + 4 f = -4.795831523 + 4 Combine like terms: -4.795831523 + 4 = -0.795831523 f = -0.795831523 Simplifying f = -0.795831523Solution
The solution to the problem is based on the solutions from the subproblems. f = {8.795831523, -0.795831523}
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