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Simplifying 33x2 + -7x + -4000 = 0 Reorder the terms: -4000 + -7x + 33x2 = 0 Solving -4000 + -7x + 33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. -121.2121212 + -0.2121212121x + x2 = 0 Move the constant term to the right: Add '121.2121212' to each side of the equation. -121.2121212 + -0.2121212121x + 121.2121212 + x2 = 0 + 121.2121212 Reorder the terms: -121.2121212 + 121.2121212 + -0.2121212121x + x2 = 0 + 121.2121212 Combine like terms: -121.2121212 + 121.2121212 = 0.0000000 0.0000000 + -0.2121212121x + x2 = 0 + 121.2121212 -0.2121212121x + x2 = 0 + 121.2121212 Combine like terms: 0 + 121.2121212 = 121.2121212 -0.2121212121x + x2 = 121.2121212 The x term is -0.2121212121x. Take half its coefficient (-0.1060606061). Square it (0.01124885217) and add it to both sides. Add '0.01124885217' to each side of the equation. -0.2121212121x + 0.01124885217 + x2 = 121.2121212 + 0.01124885217 Reorder the terms: 0.01124885217 + -0.2121212121x + x2 = 121.2121212 + 0.01124885217 Combine like terms: 121.2121212 + 0.01124885217 = 121.22337005217 0.01124885217 + -0.2121212121x + x2 = 121.22337005217 Factor a perfect square on the left side: (x + -0.1060606061)(x + -0.1060606061) = 121.22337005217 Calculate the square root of the right side: 11.010148503 Break this problem into two subproblems by setting (x + -0.1060606061) equal to 11.010148503 and -11.010148503.Subproblem 1
x + -0.1060606061 = 11.010148503 Simplifying x + -0.1060606061 = 11.010148503 Reorder the terms: -0.1060606061 + x = 11.010148503 Solving -0.1060606061 + x = 11.010148503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1060606061' to each side of the equation. -0.1060606061 + 0.1060606061 + x = 11.010148503 + 0.1060606061 Combine like terms: -0.1060606061 + 0.1060606061 = 0.0000000000 0.0000000000 + x = 11.010148503 + 0.1060606061 x = 11.010148503 + 0.1060606061 Combine like terms: 11.010148503 + 0.1060606061 = 11.1162091091 x = 11.1162091091 Simplifying x = 11.1162091091Subproblem 2
x + -0.1060606061 = -11.010148503 Simplifying x + -0.1060606061 = -11.010148503 Reorder the terms: -0.1060606061 + x = -11.010148503 Solving -0.1060606061 + x = -11.010148503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1060606061' to each side of the equation. -0.1060606061 + 0.1060606061 + x = -11.010148503 + 0.1060606061 Combine like terms: -0.1060606061 + 0.1060606061 = 0.0000000000 0.0000000000 + x = -11.010148503 + 0.1060606061 x = -11.010148503 + 0.1060606061 Combine like terms: -11.010148503 + 0.1060606061 = -10.9040878969 x = -10.9040878969 Simplifying x = -10.9040878969Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.1162091091, -10.9040878969}
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