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Simplifying 5b2 + 7b = 10 Reorder the terms: 7b + 5b2 = 10 Solving 7b + 5b2 = 10 Solving for variable 'b'. Reorder the terms: -10 + 7b + 5b2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 7b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + 1.4b + b2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.4b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + 1.4b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.4b + b2 = 0 + 2 1.4b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.4b + b2 = 2 The b term is 1.4b. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4b + 0.49 + b2 = 2 + 0.49 Reorder the terms: 0.49 + 1.4b + b2 = 2 + 0.49 Combine like terms: 2 + 0.49 = 2.49 0.49 + 1.4b + b2 = 2.49 Factor a perfect square on the left side: (b + 0.7)(b + 0.7) = 2.49 Calculate the square root of the right side: 1.577973384 Break this problem into two subproblems by setting (b + 0.7) equal to 1.577973384 and -1.577973384.Subproblem 1
b + 0.7 = 1.577973384 Simplifying b + 0.7 = 1.577973384 Reorder the terms: 0.7 + b = 1.577973384 Solving 0.7 + b = 1.577973384 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + b = 1.577973384 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + b = 1.577973384 + -0.7 b = 1.577973384 + -0.7 Combine like terms: 1.577973384 + -0.7 = 0.877973384 b = 0.877973384 Simplifying b = 0.877973384Subproblem 2
b + 0.7 = -1.577973384 Simplifying b + 0.7 = -1.577973384 Reorder the terms: 0.7 + b = -1.577973384 Solving 0.7 + b = -1.577973384 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + b = -1.577973384 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + b = -1.577973384 + -0.7 b = -1.577973384 + -0.7 Combine like terms: -1.577973384 + -0.7 = -2.277973384 b = -2.277973384 Simplifying b = -2.277973384Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.877973384, -2.277973384}
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