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Simplifying 81X2 + -43X = 76 Reorder the terms: -43X + 81X2 = 76 Solving -43X + 81X2 = 76 Solving for variable 'X'. Reorder the terms: -76 + -43X + 81X2 = 76 + -76 Combine like terms: 76 + -76 = 0 -76 + -43X + 81X2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.9382716049 + -0.5308641975X + X2 = 0 Move the constant term to the right: Add '0.9382716049' to each side of the equation. -0.9382716049 + -0.5308641975X + 0.9382716049 + X2 = 0 + 0.9382716049 Reorder the terms: -0.9382716049 + 0.9382716049 + -0.5308641975X + X2 = 0 + 0.9382716049 Combine like terms: -0.9382716049 + 0.9382716049 = 0.0000000000 0.0000000000 + -0.5308641975X + X2 = 0 + 0.9382716049 -0.5308641975X + X2 = 0 + 0.9382716049 Combine like terms: 0 + 0.9382716049 = 0.9382716049 -0.5308641975X + X2 = 0.9382716049 The X term is -0.5308641975X. Take half its coefficient (-0.2654320988). Square it (0.07045419907) and add it to both sides. Add '0.07045419907' to each side of the equation. -0.5308641975X + 0.07045419907 + X2 = 0.9382716049 + 0.07045419907 Reorder the terms: 0.07045419907 + -0.5308641975X + X2 = 0.9382716049 + 0.07045419907 Combine like terms: 0.9382716049 + 0.07045419907 = 1.00872580397 0.07045419907 + -0.5308641975X + X2 = 1.00872580397 Factor a perfect square on the left side: (X + -0.2654320988)(X + -0.2654320988) = 1.00872580397 Calculate the square root of the right side: 1.004353426 Break this problem into two subproblems by setting (X + -0.2654320988) equal to 1.004353426 and -1.004353426.Subproblem 1
X + -0.2654320988 = 1.004353426 Simplifying X + -0.2654320988 = 1.004353426 Reorder the terms: -0.2654320988 + X = 1.004353426 Solving -0.2654320988 + X = 1.004353426 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.2654320988' to each side of the equation. -0.2654320988 + 0.2654320988 + X = 1.004353426 + 0.2654320988 Combine like terms: -0.2654320988 + 0.2654320988 = 0.0000000000 0.0000000000 + X = 1.004353426 + 0.2654320988 X = 1.004353426 + 0.2654320988 Combine like terms: 1.004353426 + 0.2654320988 = 1.2697855248 X = 1.2697855248 Simplifying X = 1.2697855248Subproblem 2
X + -0.2654320988 = -1.004353426 Simplifying X + -0.2654320988 = -1.004353426 Reorder the terms: -0.2654320988 + X = -1.004353426 Solving -0.2654320988 + X = -1.004353426 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.2654320988' to each side of the equation. -0.2654320988 + 0.2654320988 + X = -1.004353426 + 0.2654320988 Combine like terms: -0.2654320988 + 0.2654320988 = 0.0000000000 0.0000000000 + X = -1.004353426 + 0.2654320988 X = -1.004353426 + 0.2654320988 Combine like terms: -1.004353426 + 0.2654320988 = -0.7389213272 X = -0.7389213272 Simplifying X = -0.7389213272Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.2697855248, -0.7389213272}
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