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Simplifying 4l2 + -7l + -130 = 0 Reorder the terms: -130 + -7l + 4l2 = 0 Solving -130 + -7l + 4l2 = 0 Solving for variable 'l'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -32.5 + -1.75l + l2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + -1.75l + 32.5 + l2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + -1.75l + l2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + -1.75l + l2 = 0 + 32.5 -1.75l + l2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 -1.75l + l2 = 32.5 The l term is -1.75l. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75l + 0.765625 + l2 = 32.5 + 0.765625 Reorder the terms: 0.765625 + -1.75l + l2 = 32.5 + 0.765625 Combine like terms: 32.5 + 0.765625 = 33.265625 0.765625 + -1.75l + l2 = 33.265625 Factor a perfect square on the left side: (l + -0.875)(l + -0.875) = 33.265625 Calculate the square root of the right side: 5.767635998 Break this problem into two subproblems by setting (l + -0.875) equal to 5.767635998 and -5.767635998.Subproblem 1
l + -0.875 = 5.767635998 Simplifying l + -0.875 = 5.767635998 Reorder the terms: -0.875 + l = 5.767635998 Solving -0.875 + l = 5.767635998 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + l = 5.767635998 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + l = 5.767635998 + 0.875 l = 5.767635998 + 0.875 Combine like terms: 5.767635998 + 0.875 = 6.642635998 l = 6.642635998 Simplifying l = 6.642635998Subproblem 2
l + -0.875 = -5.767635998 Simplifying l + -0.875 = -5.767635998 Reorder the terms: -0.875 + l = -5.767635998 Solving -0.875 + l = -5.767635998 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + l = -5.767635998 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + l = -5.767635998 + 0.875 l = -5.767635998 + 0.875 Combine like terms: -5.767635998 + 0.875 = -4.892635998 l = -4.892635998 Simplifying l = -4.892635998Solution
The solution to the problem is based on the solutions from the subproblems. l = {6.642635998, -4.892635998}
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