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Simplifying -2.01x2 + 77.84x + -613.03 = 0 Reorder the terms: -613.03 + 77.84x + -2.01x2 = 0 Solving -613.03 + 77.84x + -2.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.01 the coefficient of the squared term: Divide each side by '-2.01'. 304.9900498 + -38.72636816x + x2 = 0 Move the constant term to the right: Add '-304.9900498' to each side of the equation. 304.9900498 + -38.72636816x + -304.9900498 + x2 = 0 + -304.9900498 Reorder the terms: 304.9900498 + -304.9900498 + -38.72636816x + x2 = 0 + -304.9900498 Combine like terms: 304.9900498 + -304.9900498 = 0.0000000 0.0000000 + -38.72636816x + x2 = 0 + -304.9900498 -38.72636816x + x2 = 0 + -304.9900498 Combine like terms: 0 + -304.9900498 = -304.9900498 -38.72636816x + x2 = -304.9900498 The x term is -38.72636816x. Take half its coefficient (-19.36318408). Square it (374.9328977) and add it to both sides. Add '374.9328977' to each side of the equation. -38.72636816x + 374.9328977 + x2 = -304.9900498 + 374.9328977 Reorder the terms: 374.9328977 + -38.72636816x + x2 = -304.9900498 + 374.9328977 Combine like terms: -304.9900498 + 374.9328977 = 69.9428479 374.9328977 + -38.72636816x + x2 = 69.9428479 Factor a perfect square on the left side: (x + -19.36318408)(x + -19.36318408) = 69.9428479 Calculate the square root of the right side: 8.363184077 Break this problem into two subproblems by setting (x + -19.36318408) equal to 8.363184077 and -8.363184077.Subproblem 1
x + -19.36318408 = 8.363184077 Simplifying x + -19.36318408 = 8.363184077 Reorder the terms: -19.36318408 + x = 8.363184077 Solving -19.36318408 + x = 8.363184077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.36318408' to each side of the equation. -19.36318408 + 19.36318408 + x = 8.363184077 + 19.36318408 Combine like terms: -19.36318408 + 19.36318408 = 0.00000000 0.00000000 + x = 8.363184077 + 19.36318408 x = 8.363184077 + 19.36318408 Combine like terms: 8.363184077 + 19.36318408 = 27.726368157 x = 27.726368157 Simplifying x = 27.726368157Subproblem 2
x + -19.36318408 = -8.363184077 Simplifying x + -19.36318408 = -8.363184077 Reorder the terms: -19.36318408 + x = -8.363184077 Solving -19.36318408 + x = -8.363184077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.36318408' to each side of the equation. -19.36318408 + 19.36318408 + x = -8.363184077 + 19.36318408 Combine like terms: -19.36318408 + 19.36318408 = 0.00000000 0.00000000 + x = -8.363184077 + 19.36318408 x = -8.363184077 + 19.36318408 Combine like terms: -8.363184077 + 19.36318408 = 11.000000003 x = 11.000000003 Simplifying x = 11.000000003Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.726368157, 11.000000003}
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