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Simplifying -2.06x2 + 77.86x + 741 = 0 Reorder the terms: 741 + 77.86x + -2.06x2 = 0 Solving 741 + 77.86x + -2.06x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.06 the coefficient of the squared term: Divide each side by '-2.06'. -359.7087379 + -37.7961165x + x2 = 0 Move the constant term to the right: Add '359.7087379' to each side of the equation. -359.7087379 + -37.7961165x + 359.7087379 + x2 = 0 + 359.7087379 Reorder the terms: -359.7087379 + 359.7087379 + -37.7961165x + x2 = 0 + 359.7087379 Combine like terms: -359.7087379 + 359.7087379 = 0.0000000 0.0000000 + -37.7961165x + x2 = 0 + 359.7087379 -37.7961165x + x2 = 0 + 359.7087379 Combine like terms: 0 + 359.7087379 = 359.7087379 -37.7961165x + x2 = 359.7087379 The x term is -37.7961165x. Take half its coefficient (-18.89805825). Square it (357.1366056) and add it to both sides. Add '357.1366056' to each side of the equation. -37.7961165x + 357.1366056 + x2 = 359.7087379 + 357.1366056 Reorder the terms: 357.1366056 + -37.7961165x + x2 = 359.7087379 + 357.1366056 Combine like terms: 359.7087379 + 357.1366056 = 716.8453435 357.1366056 + -37.7961165x + x2 = 716.8453435 Factor a perfect square on the left side: (x + -18.89805825)(x + -18.89805825) = 716.8453435 Calculate the square root of the right side: 26.773967646 Break this problem into two subproblems by setting (x + -18.89805825) equal to 26.773967646 and -26.773967646.Subproblem 1
x + -18.89805825 = 26.773967646 Simplifying x + -18.89805825 = 26.773967646 Reorder the terms: -18.89805825 + x = 26.773967646 Solving -18.89805825 + x = 26.773967646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.89805825' to each side of the equation. -18.89805825 + 18.89805825 + x = 26.773967646 + 18.89805825 Combine like terms: -18.89805825 + 18.89805825 = 0.00000000 0.00000000 + x = 26.773967646 + 18.89805825 x = 26.773967646 + 18.89805825 Combine like terms: 26.773967646 + 18.89805825 = 45.672025896 x = 45.672025896 Simplifying x = 45.672025896Subproblem 2
x + -18.89805825 = -26.773967646 Simplifying x + -18.89805825 = -26.773967646 Reorder the terms: -18.89805825 + x = -26.773967646 Solving -18.89805825 + x = -26.773967646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.89805825' to each side of the equation. -18.89805825 + 18.89805825 + x = -26.773967646 + 18.89805825 Combine like terms: -18.89805825 + 18.89805825 = 0.00000000 0.00000000 + x = -26.773967646 + 18.89805825 x = -26.773967646 + 18.89805825 Combine like terms: -26.773967646 + 18.89805825 = -7.875909396 x = -7.875909396 Simplifying x = -7.875909396Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.672025896, -7.875909396}
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