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Simplifying (b2 + -2b + -35 * 2) * 3b = 0 Multiply -35 * 2 (b2 + -2b + -70) * 3b = 0 Reorder the terms: (-70 + -2b + b2) * 3b = 0 Reorder the terms for easier multiplication: 3b(-70 + -2b + b2) = 0 (-70 * 3b + -2b * 3b + b2 * 3b) = 0 (-210b + -6b2 + 3b3) = 0 Solving -210b + -6b2 + 3b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3b'. 3b(-70 + -2b + b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(-70 + -2b + b2)' equal to zero and attempt to solve: Simplifying -70 + -2b + b2 = 0 Solving -70 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -2b + 70 + b2 = 0 + 70 Reorder the terms: -70 + 70 + -2b + b2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -2b + b2 = 0 + 70 -2b + b2 = 0 + 70 Combine like terms: 0 + 70 = 70 -2b + b2 = 70 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 70 + 1 Reorder the terms: 1 + -2b + b2 = 70 + 1 Combine like terms: 70 + 1 = 71 1 + -2b + b2 = 71 Factor a perfect square on the left side: (b + -1)(b + -1) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (b + -1) equal to 8.426149773 and -8.426149773.Subproblem 1
b + -1 = 8.426149773 Simplifying b + -1 = 8.426149773 Reorder the terms: -1 + b = 8.426149773 Solving -1 + b = 8.426149773 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 8.426149773 + 1 Combine like terms: -1 + 1 = 0 0 + b = 8.426149773 + 1 b = 8.426149773 + 1 Combine like terms: 8.426149773 + 1 = 9.426149773 b = 9.426149773 Simplifying b = 9.426149773Subproblem 2
b + -1 = -8.426149773 Simplifying b + -1 = -8.426149773 Reorder the terms: -1 + b = -8.426149773 Solving -1 + b = -8.426149773 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -8.426149773 + 1 Combine like terms: -1 + 1 = 0 0 + b = -8.426149773 + 1 b = -8.426149773 + 1 Combine like terms: -8.426149773 + 1 = -7.426149773 b = -7.426149773 Simplifying b = -7.426149773Solution
The solution to the problem is based on the solutions from the subproblems. b = {9.426149773, -7.426149773}Solution
b = {0, 9.426149773, -7.426149773}
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