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Simplifying 289 = b2 + -1(b + -7) Reorder the terms: 289 = b2 + -1(-7 + b) 289 = b2 + (-7 * -1 + b * -1) 289 = b2 + (7 + -1b) Reorder the terms: 289 = 7 + -1b + b2 Solving 289 = 7 + -1b + b2 Solving for variable 'b'. Combine like terms: 289 + -7 = 282 282 + b + -1b2 = 7 + -1b + b2 + -7 + b + -1b2 Reorder the terms: 282 + b + -1b2 = 7 + -7 + -1b + b + b2 + -1b2 Combine like terms: 7 + -7 = 0 282 + b + -1b2 = 0 + -1b + b + b2 + -1b2 282 + b + -1b2 = -1b + b + b2 + -1b2 Combine like terms: -1b + b = 0 282 + b + -1b2 = 0 + b2 + -1b2 282 + b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 282 + b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -282 + -1b + b2 = 0 Move the constant term to the right: Add '282' to each side of the equation. -282 + -1b + 282 + b2 = 0 + 282 Reorder the terms: -282 + 282 + -1b + b2 = 0 + 282 Combine like terms: -282 + 282 = 0 0 + -1b + b2 = 0 + 282 -1b + b2 = 0 + 282 Combine like terms: 0 + 282 = 282 -1b + b2 = 282 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. -1b + 0.25 + b2 = 282 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 282 + 0.25 Combine like terms: 282 + 0.25 = 282.25 0.25 + -1b + b2 = 282.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (b + 0.5) equal to 16.800297616 and -16.800297616.Subproblem 1
b + 0.5 = 16.800297616 Simplifying b + 0.5 = 16.800297616 Reorder the terms: 0.5 + b = 16.800297616 Solving 0.5 + b = 16.800297616 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 = 16.800297616 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 16.800297616 + -0.5 b = 16.800297616 + -0.5 Combine like terms: 16.800297616 + -0.5 = 16.300297616 b = 16.300297616 Simplifying b = 16.300297616Subproblem 2
b + 0.5 = -16.800297616 Simplifying b + 0.5 = -16.800297616 Reorder the terms: 0.5 + b = -16.800297616 Solving 0.5 + b = -16.800297616 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 = -16.800297616 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -16.800297616 + -0.5 b = -16.800297616 + -0.5 Combine like terms: -16.800297616 + -0.5 = -17.300297616 b = -17.300297616 Simplifying b = -17.300297616Solution
The solution to the problem is based on the solutions from the subproblems. b = {16.300297616, -17.300297616}
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