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Simplifying X2 + 9X + X2 + 90 = 180 Reorder the terms: 90 + 9X + X2 + X2 = 180 Combine like terms: X2 + X2 = 2X2 90 + 9X + 2X2 = 180 Solving 90 + 9X + 2X2 = 180 Solving for variable 'X'. Reorder the terms: 90 + -180 + 9X + 2X2 = 180 + -180 Combine like terms: 90 + -180 = -90 -90 + 9X + 2X2 = 180 + -180 Combine like terms: 180 + -180 = 0 -90 + 9X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -45 + 4.5X + X2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 4.5X + 45 + X2 = 0 + 45 Reorder the terms: -45 + 45 + 4.5X + X2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 4.5X + X2 = 0 + 45 4.5X + X2 = 0 + 45 Combine like terms: 0 + 45 = 45 4.5X + X2 = 45 The X term is 4.5X. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5X + 5.0625 + X2 = 45 + 5.0625 Reorder the terms: 5.0625 + 4.5X + X2 = 45 + 5.0625 Combine like terms: 45 + 5.0625 = 50.0625 5.0625 + 4.5X + X2 = 50.0625 Factor a perfect square on the left side: (X + 2.25)(X + 2.25) = 50.0625 Calculate the square root of the right side: 7.075485849 Break this problem into two subproblems by setting (X + 2.25) equal to 7.075485849 and -7.075485849.Subproblem 1
X + 2.25 = 7.075485849 Simplifying X + 2.25 = 7.075485849 Reorder the terms: 2.25 + X = 7.075485849 Solving 2.25 + X = 7.075485849 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + X = 7.075485849 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + X = 7.075485849 + -2.25 X = 7.075485849 + -2.25 Combine like terms: 7.075485849 + -2.25 = 4.825485849 X = 4.825485849 Simplifying X = 4.825485849Subproblem 2
X + 2.25 = -7.075485849 Simplifying X + 2.25 = -7.075485849 Reorder the terms: 2.25 + X = -7.075485849 Solving 2.25 + X = -7.075485849 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + X = -7.075485849 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + X = -7.075485849 + -2.25 X = -7.075485849 + -2.25 Combine like terms: -7.075485849 + -2.25 = -9.325485849 X = -9.325485849 Simplifying X = -9.325485849Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.825485849, -9.325485849}
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