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Simplifying 17b2 + -14b + -56 = 0 Reorder the terms: -56 + -14b + 17b2 = 0 Solving -56 + -14b + 17b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -3.294117647 + -0.8235294118b + b2 = 0 Move the constant term to the right: Add '3.294117647' to each side of the equation. -3.294117647 + -0.8235294118b + 3.294117647 + b2 = 0 + 3.294117647 Reorder the terms: -3.294117647 + 3.294117647 + -0.8235294118b + b2 = 0 + 3.294117647 Combine like terms: -3.294117647 + 3.294117647 = 0.000000000 0.000000000 + -0.8235294118b + b2 = 0 + 3.294117647 -0.8235294118b + b2 = 0 + 3.294117647 Combine like terms: 0 + 3.294117647 = 3.294117647 -0.8235294118b + b2 = 3.294117647 The b term is -0.8235294118b. Take half its coefficient (-0.4117647059). Square it (0.1695501730) and add it to both sides. Add '0.1695501730' to each side of the equation. -0.8235294118b + 0.1695501730 + b2 = 3.294117647 + 0.1695501730 Reorder the terms: 0.1695501730 + -0.8235294118b + b2 = 3.294117647 + 0.1695501730 Combine like terms: 3.294117647 + 0.1695501730 = 3.46366782 0.1695501730 + -0.8235294118b + b2 = 3.46366782 Factor a perfect square on the left side: (b + -0.4117647059)(b + -0.4117647059) = 3.46366782 Calculate the square root of the right side: 1.861093179 Break this problem into two subproblems by setting (b + -0.4117647059) equal to 1.861093179 and -1.861093179.Subproblem 1
b + -0.4117647059 = 1.861093179 Simplifying b + -0.4117647059 = 1.861093179 Reorder the terms: -0.4117647059 + b = 1.861093179 Solving -0.4117647059 + b = 1.861093179 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4117647059' to each side of the equation. -0.4117647059 + 0.4117647059 + b = 1.861093179 + 0.4117647059 Combine like terms: -0.4117647059 + 0.4117647059 = 0.0000000000 0.0000000000 + b = 1.861093179 + 0.4117647059 b = 1.861093179 + 0.4117647059 Combine like terms: 1.861093179 + 0.4117647059 = 2.2728578849 b = 2.2728578849 Simplifying b = 2.2728578849Subproblem 2
b + -0.4117647059 = -1.861093179 Simplifying b + -0.4117647059 = -1.861093179 Reorder the terms: -0.4117647059 + b = -1.861093179 Solving -0.4117647059 + b = -1.861093179 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4117647059' to each side of the equation. -0.4117647059 + 0.4117647059 + b = -1.861093179 + 0.4117647059 Combine like terms: -0.4117647059 + 0.4117647059 = 0.0000000000 0.0000000000 + b = -1.861093179 + 0.4117647059 b = -1.861093179 + 0.4117647059 Combine like terms: -1.861093179 + 0.4117647059 = -1.4493284731 b = -1.4493284731 Simplifying b = -1.4493284731Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.2728578849, -1.4493284731}
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