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Simplifying 5b2 + -16b = 32 Reorder the terms: -16b + 5b2 = 32 Solving -16b + 5b2 = 32 Solving for variable 'b'. Reorder the terms: -32 + -16b + 5b2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -16b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.4 + -3.2b + b2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + -3.2b + 6.4 + b2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + -3.2b + b2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + -3.2b + b2 = 0 + 6.4 -3.2b + b2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 -3.2b + b2 = 6.4 The b term is -3.2b. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2b + 2.56 + b2 = 6.4 + 2.56 Reorder the terms: 2.56 + -3.2b + b2 = 6.4 + 2.56 Combine like terms: 6.4 + 2.56 = 8.96 2.56 + -3.2b + b2 = 8.96 Factor a perfect square on the left side: (b + -1.6)(b + -1.6) = 8.96 Calculate the square root of the right side: 2.993325909 Break this problem into two subproblems by setting (b + -1.6) equal to 2.993325909 and -2.993325909.Subproblem 1
b + -1.6 = 2.993325909 Simplifying b + -1.6 = 2.993325909 Reorder the terms: -1.6 + b = 2.993325909 Solving -1.6 + b = 2.993325909 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + b = 2.993325909 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + b = 2.993325909 + 1.6 b = 2.993325909 + 1.6 Combine like terms: 2.993325909 + 1.6 = 4.593325909 b = 4.593325909 Simplifying b = 4.593325909Subproblem 2
b + -1.6 = -2.993325909 Simplifying b + -1.6 = -2.993325909 Reorder the terms: -1.6 + b = -2.993325909 Solving -1.6 + b = -2.993325909 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + b = -2.993325909 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + b = -2.993325909 + 1.6 b = -2.993325909 + 1.6 Combine like terms: -2.993325909 + 1.6 = -1.393325909 b = -1.393325909 Simplifying b = -1.393325909Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.593325909, -1.393325909}
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