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Simplifying 7b2 + -2b + -10 = 0 Reorder the terms: -10 + -2b + 7b2 = 0 Solving -10 + -2b + 7b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + -0.2857142857b + b2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -0.2857142857b + 1.428571429 + b2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -0.2857142857b + b2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -0.2857142857b + b2 = 0 + 1.428571429 -0.2857142857b + b2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -0.2857142857b + b2 = 1.428571429 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 = 1.428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857b + b2 = 1.428571429 + 0.02040816328 Combine like terms: 1.428571429 + 0.02040816328 = 1.44897959228 0.02040816328 + -0.2857142857b + b2 = 1.44897959228 Factor a perfect square on the left side: (b + -0.1428571429)(b + -0.1428571429) = 1.44897959228 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (b + -0.1428571429) equal to 1.203735682 and -1.203735682.Subproblem 1
b + -0.1428571429 = 1.203735682 Simplifying b + -0.1428571429 = 1.203735682 Reorder the terms: -0.1428571429 + b = 1.203735682 Solving -0.1428571429 + b = 1.203735682 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 = 1.203735682 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + b = 1.203735682 + 0.1428571429 b = 1.203735682 + 0.1428571429 Combine like terms: 1.203735682 + 0.1428571429 = 1.3465928249 b = 1.3465928249 Simplifying b = 1.3465928249Subproblem 2
b + -0.1428571429 = -1.203735682 Simplifying b + -0.1428571429 = -1.203735682 Reorder the terms: -0.1428571429 + b = -1.203735682 Solving -0.1428571429 + b = -1.203735682 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 = -1.203735682 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + b = -1.203735682 + 0.1428571429 b = -1.203735682 + 0.1428571429 Combine like terms: -1.203735682 + 0.1428571429 = -1.0608785391 b = -1.0608785391 Simplifying b = -1.0608785391Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.3465928249, -1.0608785391}
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