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Simplifying 144 = b2 + -12b Reorder the terms: 144 = -12b + b2 Solving 144 = -12b + b2 Solving for variable 'b'. Reorder the terms: 144 + 12b + -1b2 = -12b + 12b + b2 + -1b2 Combine like terms: -12b + 12b = 0 144 + 12b + -1b2 = 0 + b2 + -1b2 144 + 12b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 144 + 12b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + -12b + b2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + -12b + 144 + b2 = 0 + 144 Reorder the terms: -144 + 144 + -12b + b2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -12b + b2 = 0 + 144 -12b + b2 = 0 + 144 Combine like terms: 0 + 144 = 144 -12b + b2 = 144 The b term is -12b. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12b + 36 + b2 = 144 + 36 Reorder the terms: 36 + -12b + b2 = 144 + 36 Combine like terms: 144 + 36 = 180 36 + -12b + b2 = 180 Factor a perfect square on the left side: (b + -6)(b + -6) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (b + -6) equal to 13.416407865 and -13.416407865.Subproblem 1
b + -6 = 13.416407865 Simplifying b + -6 = 13.416407865 Reorder the terms: -6 + b = 13.416407865 Solving -6 + b = 13.416407865 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = 13.416407865 + 6 Combine like terms: -6 + 6 = 0 0 + b = 13.416407865 + 6 b = 13.416407865 + 6 Combine like terms: 13.416407865 + 6 = 19.416407865 b = 19.416407865 Simplifying b = 19.416407865Subproblem 2
b + -6 = -13.416407865 Simplifying b + -6 = -13.416407865 Reorder the terms: -6 + b = -13.416407865 Solving -6 + b = -13.416407865 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = -13.416407865 + 6 Combine like terms: -6 + 6 = 0 0 + b = -13.416407865 + 6 b = -13.416407865 + 6 Combine like terms: -13.416407865 + 6 = -7.416407865 b = -7.416407865 Simplifying b = -7.416407865Solution
The solution to the problem is based on the solutions from the subproblems. b = {19.416407865, -7.416407865}
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