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Simplifying 0 = X2 + -18X + -45 Reorder the terms: 0 = -45 + -18X + X2 Solving 0 = -45 + -18X + X2 Solving for variable 'X'. Combine like terms: 0 + 45 = 45 45 + 18X + -1X2 = -45 + -18X + X2 + 45 + 18X + -1X2 Reorder the terms: 45 + 18X + -1X2 = -45 + 45 + -18X + 18X + X2 + -1X2 Combine like terms: -45 + 45 = 0 45 + 18X + -1X2 = 0 + -18X + 18X + X2 + -1X2 45 + 18X + -1X2 = -18X + 18X + X2 + -1X2 Combine like terms: -18X + 18X = 0 45 + 18X + -1X2 = 0 + X2 + -1X2 45 + 18X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 45 + 18X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + -18X + X2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -18X + 45 + X2 = 0 + 45 Reorder the terms: -45 + 45 + -18X + X2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -18X + X2 = 0 + 45 -18X + X2 = 0 + 45 Combine like terms: 0 + 45 = 45 -18X + X2 = 45 The X term is -18X. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18X + 81 + X2 = 45 + 81 Reorder the terms: 81 + -18X + X2 = 45 + 81 Combine like terms: 45 + 81 = 126 81 + -18X + X2 = 126 Factor a perfect square on the left side: (X + -9)(X + -9) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (X + -9) equal to 11.22497216 and -11.22497216.Subproblem 1
X + -9 = 11.22497216 Simplifying X + -9 = 11.22497216 Reorder the terms: -9 + X = 11.22497216 Solving -9 + X = 11.22497216 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + X = 11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + X = 11.22497216 + 9 X = 11.22497216 + 9 Combine like terms: 11.22497216 + 9 = 20.22497216 X = 20.22497216 Simplifying X = 20.22497216Subproblem 2
X + -9 = -11.22497216 Simplifying X + -9 = -11.22497216 Reorder the terms: -9 + X = -11.22497216 Solving -9 + X = -11.22497216 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + X = -11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + X = -11.22497216 + 9 X = -11.22497216 + 9 Combine like terms: -11.22497216 + 9 = -2.22497216 X = -2.22497216 Simplifying X = -2.22497216Solution
The solution to the problem is based on the solutions from the subproblems. X = {20.22497216, -2.22497216}
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