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Simplifying 12x2 + 84x + -121 = 0 Reorder the terms: -121 + 84x + 12x2 = 0 Solving -121 + 84x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -10.08333333 + 7x + x2 = 0 Move the constant term to the right: Add '10.08333333' to each side of the equation. -10.08333333 + 7x + 10.08333333 + x2 = 0 + 10.08333333 Reorder the terms: -10.08333333 + 10.08333333 + 7x + x2 = 0 + 10.08333333 Combine like terms: -10.08333333 + 10.08333333 = 0.00000000 0.00000000 + 7x + x2 = 0 + 10.08333333 7x + x2 = 0 + 10.08333333 Combine like terms: 0 + 10.08333333 = 10.08333333 7x + x2 = 10.08333333 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 10.08333333 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 10.08333333 + 12.25 Combine like terms: 10.08333333 + 12.25 = 22.33333333 12.25 + 7x + x2 = 22.33333333 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 22.33333333 Calculate the square root of the right side: 4.725815626 Break this problem into two subproblems by setting (x + 3.5) equal to 4.725815626 and -4.725815626.Subproblem 1
x + 3.5 = 4.725815626 Simplifying x + 3.5 = 4.725815626 Reorder the terms: 3.5 + x = 4.725815626 Solving 3.5 + x = 4.725815626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.725815626 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.725815626 + -3.5 x = 4.725815626 + -3.5 Combine like terms: 4.725815626 + -3.5 = 1.225815626 x = 1.225815626 Simplifying x = 1.225815626Subproblem 2
x + 3.5 = -4.725815626 Simplifying x + 3.5 = -4.725815626 Reorder the terms: 3.5 + x = -4.725815626 Solving 3.5 + x = -4.725815626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.725815626 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.725815626 + -3.5 x = -4.725815626 + -3.5 Combine like terms: -4.725815626 + -3.5 = -8.225815626 x = -8.225815626 Simplifying x = -8.225815626Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.225815626, -8.225815626}
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