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Simplifying 13x2 + -840x + -5040 = 0 Reorder the terms: -5040 + -840x + 13x2 = 0 Solving -5040 + -840x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -387.6923077 + -64.61538462x + x2 = 0 Move the constant term to the right: Add '387.6923077' to each side of the equation. -387.6923077 + -64.61538462x + 387.6923077 + x2 = 0 + 387.6923077 Reorder the terms: -387.6923077 + 387.6923077 + -64.61538462x + x2 = 0 + 387.6923077 Combine like terms: -387.6923077 + 387.6923077 = 0.0000000 0.0000000 + -64.61538462x + x2 = 0 + 387.6923077 -64.61538462x + x2 = 0 + 387.6923077 Combine like terms: 0 + 387.6923077 = 387.6923077 -64.61538462x + x2 = 387.6923077 The x term is -64.61538462x. Take half its coefficient (-32.30769231). Square it (1043.786982) and add it to both sides. Add '1043.786982' to each side of the equation. -64.61538462x + 1043.786982 + x2 = 387.6923077 + 1043.786982 Reorder the terms: 1043.786982 + -64.61538462x + x2 = 387.6923077 + 1043.786982 Combine like terms: 387.6923077 + 1043.786982 = 1431.4792897 1043.786982 + -64.61538462x + x2 = 1431.4792897 Factor a perfect square on the left side: (x + -32.30769231)(x + -32.30769231) = 1431.4792897 Calculate the square root of the right side: 37.834895133 Break this problem into two subproblems by setting (x + -32.30769231) equal to 37.834895133 and -37.834895133.Subproblem 1
x + -32.30769231 = 37.834895133 Simplifying x + -32.30769231 = 37.834895133 Reorder the terms: -32.30769231 + x = 37.834895133 Solving -32.30769231 + x = 37.834895133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.30769231' to each side of the equation. -32.30769231 + 32.30769231 + x = 37.834895133 + 32.30769231 Combine like terms: -32.30769231 + 32.30769231 = 0.00000000 0.00000000 + x = 37.834895133 + 32.30769231 x = 37.834895133 + 32.30769231 Combine like terms: 37.834895133 + 32.30769231 = 70.142587443 x = 70.142587443 Simplifying x = 70.142587443Subproblem 2
x + -32.30769231 = -37.834895133 Simplifying x + -32.30769231 = -37.834895133 Reorder the terms: -32.30769231 + x = -37.834895133 Solving -32.30769231 + x = -37.834895133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.30769231' to each side of the equation. -32.30769231 + 32.30769231 + x = -37.834895133 + 32.30769231 Combine like terms: -32.30769231 + 32.30769231 = 0.00000000 0.00000000 + x = -37.834895133 + 32.30769231 x = -37.834895133 + 32.30769231 Combine like terms: -37.834895133 + 32.30769231 = -5.527202823 x = -5.527202823 Simplifying x = -5.527202823Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.142587443, -5.527202823}
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