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Simplifying 2b(2b) + 4b + -70 = 0 Remove parenthesis around (2b) 2b * 2b + 4b + -70 = 0 Reorder the terms for easier multiplication: 2 * 2b * b + 4b + -70 = 0 Multiply 2 * 2 4b * b + 4b + -70 = 0 Multiply b * b 4b2 + 4b + -70 = 0 Reorder the terms: -70 + 4b + 4b2 = 0 Solving -70 + 4b + 4b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 2b + 2b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + 2b + 2b2)' equal to zero and attempt to solve: Simplifying -35 + 2b + 2b2 = 0 Solving -35 + 2b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + b + b2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + b + 17.5 + b2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + b + b2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + b + b2 = 0 + 17.5 b + b2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 b + b2 = 17.5 The b term is b. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + b2 = 17.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + b2 = 17.5 + 0.25 Combine like terms: 17.5 + 0.25 = 17.75 1.25 + b2 = 17.75 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (b + 0.5) equal to 4.213074887 and -4.213074887.Subproblem 1
b + 0.5 = 4.213074887 Simplifying b + 0.5 = 4.213074887 Reorder the terms: 0.5 + b = 4.213074887 Solving 0.5 + b = 4.213074887 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 4.213074887 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 4.213074887 + -0.5 b = 4.213074887 + -0.5 Combine like terms: 4.213074887 + -0.5 = 3.713074887 b = 3.713074887 Simplifying b = 3.713074887Subproblem 2
b + 0.5 = -4.213074887 Simplifying b + 0.5 = -4.213074887 Reorder the terms: 0.5 + b = -4.213074887 Solving 0.5 + b = -4.213074887 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -4.213074887 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -4.213074887 + -0.5 b = -4.213074887 + -0.5 Combine like terms: -4.213074887 + -0.5 = -4.713074887 b = -4.713074887 Simplifying b = -4.713074887Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.713074887, -4.713074887}Solution
b = {3.713074887, -4.713074887}
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