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Simplifying 21x2 + 41x = -1 Reorder the terms: 41x + 21x2 = -1 Solving 41x + 21x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 41x + 21x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 41x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.04761904762 + 1.952380952x + x2 = 0 Move the constant term to the right: Add '-0.04761904762' to each side of the equation. 0.04761904762 + 1.952380952x + -0.04761904762 + x2 = 0 + -0.04761904762 Reorder the terms: 0.04761904762 + -0.04761904762 + 1.952380952x + x2 = 0 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + 1.952380952x + x2 = 0 + -0.04761904762 1.952380952x + x2 = 0 + -0.04761904762 Combine like terms: 0 + -0.04761904762 = -0.04761904762 1.952380952x + x2 = -0.04761904762 The x term is 1.952380952x. Take half its coefficient (0.976190476). Square it (0.9529478454) and add it to both sides. Add '0.9529478454' to each side of the equation. 1.952380952x + 0.9529478454 + x2 = -0.04761904762 + 0.9529478454 Reorder the terms: 0.9529478454 + 1.952380952x + x2 = -0.04761904762 + 0.9529478454 Combine like terms: -0.04761904762 + 0.9529478454 = 0.90532879778 0.9529478454 + 1.952380952x + x2 = 0.90532879778 Factor a perfect square on the left side: (x + 0.976190476)(x + 0.976190476) = 0.90532879778 Calculate the square root of the right side: 0.951487676 Break this problem into two subproblems by setting (x + 0.976190476) equal to 0.951487676 and -0.951487676.Subproblem 1
x + 0.976190476 = 0.951487676 Simplifying x + 0.976190476 = 0.951487676 Reorder the terms: 0.976190476 + x = 0.951487676 Solving 0.976190476 + x = 0.951487676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.976190476' to each side of the equation. 0.976190476 + -0.976190476 + x = 0.951487676 + -0.976190476 Combine like terms: 0.976190476 + -0.976190476 = 0.000000000 0.000000000 + x = 0.951487676 + -0.976190476 x = 0.951487676 + -0.976190476 Combine like terms: 0.951487676 + -0.976190476 = -0.0247028 x = -0.0247028 Simplifying x = -0.0247028Subproblem 2
x + 0.976190476 = -0.951487676 Simplifying x + 0.976190476 = -0.951487676 Reorder the terms: 0.976190476 + x = -0.951487676 Solving 0.976190476 + x = -0.951487676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.976190476' to each side of the equation. 0.976190476 + -0.976190476 + x = -0.951487676 + -0.976190476 Combine like terms: 0.976190476 + -0.976190476 = 0.000000000 0.000000000 + x = -0.951487676 + -0.976190476 x = -0.951487676 + -0.976190476 Combine like terms: -0.951487676 + -0.976190476 = -1.927678152 x = -1.927678152 Simplifying x = -1.927678152Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0247028, -1.927678152}
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