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Simplifying 0 = x2 + -60x + 18 Reorder the terms: 0 = 18 + -60x + x2 Solving 0 = 18 + -60x + x2 Solving for variable 'x'. Combine like terms: 0 + -18 = -18 -18 + 60x + -1x2 = 18 + -60x + x2 + -18 + 60x + -1x2 Reorder the terms: -18 + 60x + -1x2 = 18 + -18 + -60x + 60x + x2 + -1x2 Combine like terms: 18 + -18 = 0 -18 + 60x + -1x2 = 0 + -60x + 60x + x2 + -1x2 -18 + 60x + -1x2 = -60x + 60x + x2 + -1x2 Combine like terms: -60x + 60x = 0 -18 + 60x + -1x2 = 0 + x2 + -1x2 -18 + 60x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -18 + 60x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 18 + -60x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -60x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -60x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -60x + x2 = 0 + -18 -60x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -60x + x2 = -18 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -18 + 900 Reorder the terms: 900 + -60x + x2 = -18 + 900 Combine like terms: -18 + 900 = 882 900 + -60x + x2 = 882 Factor a perfect square on the left side: (x + -30)(x + -30) = 882 Calculate the square root of the right side: 29.69848481 Break this problem into two subproblems by setting (x + -30) equal to 29.69848481 and -29.69848481.Subproblem 1
x + -30 = 29.69848481 Simplifying x + -30 = 29.69848481 Reorder the terms: -30 + x = 29.69848481 Solving -30 + x = 29.69848481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 29.69848481 + 30 Combine like terms: -30 + 30 = 0 0 + x = 29.69848481 + 30 x = 29.69848481 + 30 Combine like terms: 29.69848481 + 30 = 59.69848481 x = 59.69848481 Simplifying x = 59.69848481Subproblem 2
x + -30 = -29.69848481 Simplifying x + -30 = -29.69848481 Reorder the terms: -30 + x = -29.69848481 Solving -30 + x = -29.69848481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -29.69848481 + 30 Combine like terms: -30 + 30 = 0 0 + x = -29.69848481 + 30 x = -29.69848481 + 30 Combine like terms: -29.69848481 + 30 = 0.30151519 x = 0.30151519 Simplifying x = 0.30151519Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.69848481, 0.30151519}
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