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Simplifying 7b2 = 2b + 22 Reorder the terms: 7b2 = 22 + 2b Solving 7b2 = 22 + 2b Solving for variable 'b'. Reorder the terms: -22 + -2b + 7b2 = 22 + 2b + -22 + -2b Reorder the terms: -22 + -2b + 7b2 = 22 + -22 + 2b + -2b Combine like terms: 22 + -22 = 0 -22 + -2b + 7b2 = 0 + 2b + -2b -22 + -2b + 7b2 = 2b + -2b Combine like terms: 2b + -2b = 0 -22 + -2b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.142857143 + -0.2857142857b + b2 = 0 Move the constant term to the right: Add '3.142857143' to each side of the equation. -3.142857143 + -0.2857142857b + 3.142857143 + b2 = 0 + 3.142857143 Reorder the terms: -3.142857143 + 3.142857143 + -0.2857142857b + b2 = 0 + 3.142857143 Combine like terms: -3.142857143 + 3.142857143 = 0.000000000 0.000000000 + -0.2857142857b + b2 = 0 + 3.142857143 -0.2857142857b + b2 = 0 + 3.142857143 Combine like terms: 0 + 3.142857143 = 3.142857143 -0.2857142857b + b2 = 3.142857143 The b term is -0.2857142857b. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857b + 0.02040816328 + b2 = 3.142857143 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857b + b2 = 3.142857143 + 0.02040816328 Combine like terms: 3.142857143 + 0.02040816328 = 3.16326530628 0.02040816328 + -0.2857142857b + b2 = 3.16326530628 Factor a perfect square on the left side: (b + -0.1428571429)(b + -0.1428571429) = 3.16326530628 Calculate the square root of the right side: 1.778557085 Break this problem into two subproblems by setting (b + -0.1428571429) equal to 1.778557085 and -1.778557085.Subproblem 1
b + -0.1428571429 = 1.778557085 Simplifying b + -0.1428571429 = 1.778557085 Reorder the terms: -0.1428571429 + b = 1.778557085 Solving -0.1428571429 + b = 1.778557085 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + b = 1.778557085 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + b = 1.778557085 + 0.1428571429 b = 1.778557085 + 0.1428571429 Combine like terms: 1.778557085 + 0.1428571429 = 1.9214142279 b = 1.9214142279 Simplifying b = 1.9214142279Subproblem 2
b + -0.1428571429 = -1.778557085 Simplifying b + -0.1428571429 = -1.778557085 Reorder the terms: -0.1428571429 + b = -1.778557085 Solving -0.1428571429 + b = -1.778557085 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + b = -1.778557085 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + b = -1.778557085 + 0.1428571429 b = -1.778557085 + 0.1428571429 Combine like terms: -1.778557085 + 0.1428571429 = -1.6356999421 b = -1.6356999421 Simplifying b = -1.6356999421Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.9214142279, -1.6356999421}
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