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Simplifying 4b2 + -8b + -7 = 0 Reorder the terms: -7 + -8b + 4b2 = 0 Solving -7 + -8b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -2b + b2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -2b + 1.75 + b2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -2b + b2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -2b + b2 = 0 + 1.75 -2b + b2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -2b + b2 = 1.75 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 = 1.75 + 1 Reorder the terms: 1 + -2b + b2 = 1.75 + 1 Combine like terms: 1.75 + 1 = 2.75 1 + -2b + b2 = 2.75 Factor a perfect square on the left side: (b + -1)(b + -1) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (b + -1) equal to 1.658312395 and -1.658312395.Subproblem 1
b + -1 = 1.658312395 Simplifying b + -1 = 1.658312395 Reorder the terms: -1 + b = 1.658312395 Solving -1 + b = 1.658312395 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 = 1.658312395 + 1 Combine like terms: -1 + 1 = 0 0 + b = 1.658312395 + 1 b = 1.658312395 + 1 Combine like terms: 1.658312395 + 1 = 2.658312395 b = 2.658312395 Simplifying b = 2.658312395Subproblem 2
b + -1 = -1.658312395 Simplifying b + -1 = -1.658312395 Reorder the terms: -1 + b = -1.658312395 Solving -1 + b = -1.658312395 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 = -1.658312395 + 1 Combine like terms: -1 + 1 = 0 0 + b = -1.658312395 + 1 b = -1.658312395 + 1 Combine like terms: -1.658312395 + 1 = -0.658312395 b = -0.658312395 Simplifying b = -0.658312395Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.658312395, -0.658312395}
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