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Simplifying 0 = 2x2 + -36x + 153 Reorder the terms: 0 = 153 + -36x + 2x2 Solving 0 = 153 + -36x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -153 = -153 -153 + 36x + -2x2 = 153 + -36x + 2x2 + -153 + 36x + -2x2 Reorder the terms: -153 + 36x + -2x2 = 153 + -153 + -36x + 36x + 2x2 + -2x2 Combine like terms: 153 + -153 = 0 -153 + 36x + -2x2 = 0 + -36x + 36x + 2x2 + -2x2 -153 + 36x + -2x2 = -36x + 36x + 2x2 + -2x2 Combine like terms: -36x + 36x = 0 -153 + 36x + -2x2 = 0 + 2x2 + -2x2 -153 + 36x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -153 + 36x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 76.5 + -18x + x2 = 0 Move the constant term to the right: Add '-76.5' to each side of the equation. 76.5 + -18x + -76.5 + x2 = 0 + -76.5 Reorder the terms: 76.5 + -76.5 + -18x + x2 = 0 + -76.5 Combine like terms: 76.5 + -76.5 = 0.0 0.0 + -18x + x2 = 0 + -76.5 -18x + x2 = 0 + -76.5 Combine like terms: 0 + -76.5 = -76.5 -18x + x2 = -76.5 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 = -76.5 + 81 Reorder the terms: 81 + -18x + x2 = -76.5 + 81 Combine like terms: -76.5 + 81 = 4.5 81 + -18x + x2 = 4.5 Factor a perfect square on the left side: (x + -9)(x + -9) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + -9) equal to 2.121320344 and -2.121320344.Subproblem 1
x + -9 = 2.121320344 Simplifying x + -9 = 2.121320344 Reorder the terms: -9 + x = 2.121320344 Solving -9 + x = 2.121320344 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 = 2.121320344 + 9 Combine like terms: -9 + 9 = 0 0 + x = 2.121320344 + 9 x = 2.121320344 + 9 Combine like terms: 2.121320344 + 9 = 11.121320344 x = 11.121320344 Simplifying x = 11.121320344Subproblem 2
x + -9 = -2.121320344 Simplifying x + -9 = -2.121320344 Reorder the terms: -9 + x = -2.121320344 Solving -9 + x = -2.121320344 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 = -2.121320344 + 9 Combine like terms: -9 + 9 = 0 0 + x = -2.121320344 + 9 x = -2.121320344 + 9 Combine like terms: -2.121320344 + 9 = 6.878679656 x = 6.878679656 Simplifying x = 6.878679656Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.121320344, 6.878679656}
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