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Simplifying 0.565145x2 + 4.49x + -90 = 0 Reorder the terms: -90 + 4.49x + 0.565145x2 = 0 Solving -90 + 4.49x + 0.565145x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.565145 the coefficient of the squared term: Divide each side by '0.565145'. -159.2511656 + 7.944863708x + x2 = 0 Move the constant term to the right: Add '159.2511656' to each side of the equation. -159.2511656 + 7.944863708x + 159.2511656 + x2 = 0 + 159.2511656 Reorder the terms: -159.2511656 + 159.2511656 + 7.944863708x + x2 = 0 + 159.2511656 Combine like terms: -159.2511656 + 159.2511656 = 0.0000000 0.0000000 + 7.944863708x + x2 = 0 + 159.2511656 7.944863708x + x2 = 0 + 159.2511656 Combine like terms: 0 + 159.2511656 = 159.2511656 7.944863708x + x2 = 159.2511656 The x term is 7.944863708x. Take half its coefficient (3.972431854). Square it (15.78021483) and add it to both sides. Add '15.78021483' to each side of the equation. 7.944863708x + 15.78021483 + x2 = 159.2511656 + 15.78021483 Reorder the terms: 15.78021483 + 7.944863708x + x2 = 159.2511656 + 15.78021483 Combine like terms: 159.2511656 + 15.78021483 = 175.03138043 15.78021483 + 7.944863708x + x2 = 175.03138043 Factor a perfect square on the left side: (x + 3.972431854)(x + 3.972431854) = 175.03138043 Calculate the square root of the right side: 13.229942571 Break this problem into two subproblems by setting (x + 3.972431854) equal to 13.229942571 and -13.229942571.Subproblem 1
x + 3.972431854 = 13.229942571 Simplifying x + 3.972431854 = 13.229942571 Reorder the terms: 3.972431854 + x = 13.229942571 Solving 3.972431854 + x = 13.229942571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.972431854' to each side of the equation. 3.972431854 + -3.972431854 + x = 13.229942571 + -3.972431854 Combine like terms: 3.972431854 + -3.972431854 = 0.000000000 0.000000000 + x = 13.229942571 + -3.972431854 x = 13.229942571 + -3.972431854 Combine like terms: 13.229942571 + -3.972431854 = 9.257510717 x = 9.257510717 Simplifying x = 9.257510717Subproblem 2
x + 3.972431854 = -13.229942571 Simplifying x + 3.972431854 = -13.229942571 Reorder the terms: 3.972431854 + x = -13.229942571 Solving 3.972431854 + x = -13.229942571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.972431854' to each side of the equation. 3.972431854 + -3.972431854 + x = -13.229942571 + -3.972431854 Combine like terms: 3.972431854 + -3.972431854 = 0.000000000 0.000000000 + x = -13.229942571 + -3.972431854 x = -13.229942571 + -3.972431854 Combine like terms: -13.229942571 + -3.972431854 = -17.202374425 x = -17.202374425 Simplifying x = -17.202374425Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.257510717, -17.202374425}
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