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Simplifying b2 + -10b + -64 = 7 Reorder the terms: -64 + -10b + b2 = 7 Solving -64 + -10b + b2 = 7 Solving for variable 'b'. Reorder the terms: -64 + -7 + -10b + b2 = 7 + -7 Combine like terms: -64 + -7 = -71 -71 + -10b + b2 = 7 + -7 Combine like terms: 7 + -7 = 0 -71 + -10b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -10b + 71 + b2 = 0 + 71 Reorder the terms: -71 + 71 + -10b + b2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -10b + b2 = 0 + 71 -10b + b2 = 0 + 71 Combine like terms: 0 + 71 = 71 -10b + b2 = 71 The b term is -10b. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10b + 25 + b2 = 71 + 25 Reorder the terms: 25 + -10b + b2 = 71 + 25 Combine like terms: 71 + 25 = 96 25 + -10b + b2 = 96 Factor a perfect square on the left side: (b + -5)(b + -5) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (b + -5) equal to 9.797958971 and -9.797958971.Subproblem 1
b + -5 = 9.797958971 Simplifying b + -5 = 9.797958971 Reorder the terms: -5 + b = 9.797958971 Solving -5 + b = 9.797958971 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + b = 9.797958971 + 5 Combine like terms: -5 + 5 = 0 0 + b = 9.797958971 + 5 b = 9.797958971 + 5 Combine like terms: 9.797958971 + 5 = 14.797958971 b = 14.797958971 Simplifying b = 14.797958971Subproblem 2
b + -5 = -9.797958971 Simplifying b + -5 = -9.797958971 Reorder the terms: -5 + b = -9.797958971 Solving -5 + b = -9.797958971 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + b = -9.797958971 + 5 Combine like terms: -5 + 5 = 0 0 + b = -9.797958971 + 5 b = -9.797958971 + 5 Combine like terms: -9.797958971 + 5 = -4.797958971 b = -4.797958971 Simplifying b = -4.797958971Solution
The solution to the problem is based on the solutions from the subproblems. b = {14.797958971, -4.797958971}
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