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Simplifying 52b2 + -23b + -63 = 0 Reorder the terms: -63 + -23b + 52b2 = 0 Solving -63 + -23b + 52b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 52 the coefficient of the squared term: Divide each side by '52'. -1.211538462 + -0.4423076923b + b2 = 0 Move the constant term to the right: Add '1.211538462' to each side of the equation. -1.211538462 + -0.4423076923b + 1.211538462 + b2 = 0 + 1.211538462 Reorder the terms: -1.211538462 + 1.211538462 + -0.4423076923b + b2 = 0 + 1.211538462 Combine like terms: -1.211538462 + 1.211538462 = 0.000000000 0.000000000 + -0.4423076923b + b2 = 0 + 1.211538462 -0.4423076923b + b2 = 0 + 1.211538462 Combine like terms: 0 + 1.211538462 = 1.211538462 -0.4423076923b + b2 = 1.211538462 The b term is -0.4423076923b. Take half its coefficient (-0.2211538462). Square it (0.04890902369) and add it to both sides. Add '0.04890902369' to each side of the equation. -0.4423076923b + 0.04890902369 + b2 = 1.211538462 + 0.04890902369 Reorder the terms: 0.04890902369 + -0.4423076923b + b2 = 1.211538462 + 0.04890902369 Combine like terms: 1.211538462 + 0.04890902369 = 1.26044748569 0.04890902369 + -0.4423076923b + b2 = 1.26044748569 Factor a perfect square on the left side: (b + -0.2211538462)(b + -0.2211538462) = 1.26044748569 Calculate the square root of the right side: 1.122696524 Break this problem into two subproblems by setting (b + -0.2211538462) equal to 1.122696524 and -1.122696524.Subproblem 1
b + -0.2211538462 = 1.122696524 Simplifying b + -0.2211538462 = 1.122696524 Reorder the terms: -0.2211538462 + b = 1.122696524 Solving -0.2211538462 + b = 1.122696524 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2211538462' to each side of the equation. -0.2211538462 + 0.2211538462 + b = 1.122696524 + 0.2211538462 Combine like terms: -0.2211538462 + 0.2211538462 = 0.0000000000 0.0000000000 + b = 1.122696524 + 0.2211538462 b = 1.122696524 + 0.2211538462 Combine like terms: 1.122696524 + 0.2211538462 = 1.3438503702 b = 1.3438503702 Simplifying b = 1.3438503702Subproblem 2
b + -0.2211538462 = -1.122696524 Simplifying b + -0.2211538462 = -1.122696524 Reorder the terms: -0.2211538462 + b = -1.122696524 Solving -0.2211538462 + b = -1.122696524 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2211538462' to each side of the equation. -0.2211538462 + 0.2211538462 + b = -1.122696524 + 0.2211538462 Combine like terms: -0.2211538462 + 0.2211538462 = 0.0000000000 0.0000000000 + b = -1.122696524 + 0.2211538462 b = -1.122696524 + 0.2211538462 Combine like terms: -1.122696524 + 0.2211538462 = -0.9015426778 b = -0.9015426778 Simplifying b = -0.9015426778Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.3438503702, -0.9015426778}
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