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Simplifying x2 + -60x + 720 = 0 Reorder the terms: 720 + -60x + x2 = 0 Solving 720 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-720' to each side of the equation. 720 + -60x + -720 + x2 = 0 + -720 Reorder the terms: 720 + -720 + -60x + x2 = 0 + -720 Combine like terms: 720 + -720 = 0 0 + -60x + x2 = 0 + -720 -60x + x2 = 0 + -720 Combine like terms: 0 + -720 = -720 -60x + x2 = -720 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 = -720 + 900 Reorder the terms: 900 + -60x + x2 = -720 + 900 Combine like terms: -720 + 900 = 180 900 + -60x + x2 = 180 Factor a perfect square on the left side: (x + -30)(x + -30) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + -30) equal to 13.416407865 and -13.416407865.Subproblem 1
x + -30 = 13.416407865 Simplifying x + -30 = 13.416407865 Reorder the terms: -30 + x = 13.416407865 Solving -30 + x = 13.416407865 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 = 13.416407865 + 30 Combine like terms: -30 + 30 = 0 0 + x = 13.416407865 + 30 x = 13.416407865 + 30 Combine like terms: 13.416407865 + 30 = 43.416407865 x = 43.416407865 Simplifying x = 43.416407865Subproblem 2
x + -30 = -13.416407865 Simplifying x + -30 = -13.416407865 Reorder the terms: -30 + x = -13.416407865 Solving -30 + x = -13.416407865 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 = -13.416407865 + 30 Combine like terms: -30 + 30 = 0 0 + x = -13.416407865 + 30 x = -13.416407865 + 30 Combine like terms: -13.416407865 + 30 = 16.583592135 x = 16.583592135 Simplifying x = 16.583592135Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.416407865, 16.583592135}
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