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Simplifying 21x2 + -121x = 40 Reorder the terms: -121x + 21x2 = 40 Solving -121x + 21x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + -121x + 21x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -121x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.904761905 + -5.761904762x + x2 = 0 Move the constant term to the right: Add '1.904761905' to each side of the equation. -1.904761905 + -5.761904762x + 1.904761905 + x2 = 0 + 1.904761905 Reorder the terms: -1.904761905 + 1.904761905 + -5.761904762x + x2 = 0 + 1.904761905 Combine like terms: -1.904761905 + 1.904761905 = 0.000000000 0.000000000 + -5.761904762x + x2 = 0 + 1.904761905 -5.761904762x + x2 = 0 + 1.904761905 Combine like terms: 0 + 1.904761905 = 1.904761905 -5.761904762x + x2 = 1.904761905 The x term is -5.761904762x. Take half its coefficient (-2.880952381). Square it (8.299886622) and add it to both sides. Add '8.299886622' to each side of the equation. -5.761904762x + 8.299886622 + x2 = 1.904761905 + 8.299886622 Reorder the terms: 8.299886622 + -5.761904762x + x2 = 1.904761905 + 8.299886622 Combine like terms: 1.904761905 + 8.299886622 = 10.204648527 8.299886622 + -5.761904762x + x2 = 10.204648527 Factor a perfect square on the left side: (x + -2.880952381)(x + -2.880952381) = 10.204648527 Calculate the square root of the right side: 3.194471557 Break this problem into two subproblems by setting (x + -2.880952381) equal to 3.194471557 and -3.194471557.Subproblem 1
x + -2.880952381 = 3.194471557 Simplifying x + -2.880952381 = 3.194471557 Reorder the terms: -2.880952381 + x = 3.194471557 Solving -2.880952381 + x = 3.194471557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.880952381' to each side of the equation. -2.880952381 + 2.880952381 + x = 3.194471557 + 2.880952381 Combine like terms: -2.880952381 + 2.880952381 = 0.000000000 0.000000000 + x = 3.194471557 + 2.880952381 x = 3.194471557 + 2.880952381 Combine like terms: 3.194471557 + 2.880952381 = 6.075423938 x = 6.075423938 Simplifying x = 6.075423938Subproblem 2
x + -2.880952381 = -3.194471557 Simplifying x + -2.880952381 = -3.194471557 Reorder the terms: -2.880952381 + x = -3.194471557 Solving -2.880952381 + x = -3.194471557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.880952381' to each side of the equation. -2.880952381 + 2.880952381 + x = -3.194471557 + 2.880952381 Combine like terms: -2.880952381 + 2.880952381 = 0.000000000 0.000000000 + x = -3.194471557 + 2.880952381 x = -3.194471557 + 2.880952381 Combine like terms: -3.194471557 + 2.880952381 = -0.313519176 x = -0.313519176 Simplifying x = -0.313519176Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.075423938, -0.313519176}
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