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Simplifying x2 + -60x + 810 = 0 Reorder the terms: 810 + -60x + x2 = 0 Solving 810 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-810' to each side of the equation. 810 + -60x + -810 + x2 = 0 + -810 Reorder the terms: 810 + -810 + -60x + x2 = 0 + -810 Combine like terms: 810 + -810 = 0 0 + -60x + x2 = 0 + -810 -60x + x2 = 0 + -810 Combine like terms: 0 + -810 = -810 -60x + x2 = -810 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 = -810 + 900 Reorder the terms: 900 + -60x + x2 = -810 + 900 Combine like terms: -810 + 900 = 90 900 + -60x + x2 = 90 Factor a perfect square on the left side: (x + -30)(x + -30) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + -30) equal to 9.486832981 and -9.486832981.Subproblem 1
x + -30 = 9.486832981 Simplifying x + -30 = 9.486832981 Reorder the terms: -30 + x = 9.486832981 Solving -30 + x = 9.486832981 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 = 9.486832981 + 30 Combine like terms: -30 + 30 = 0 0 + x = 9.486832981 + 30 x = 9.486832981 + 30 Combine like terms: 9.486832981 + 30 = 39.486832981 x = 39.486832981 Simplifying x = 39.486832981Subproblem 2
x + -30 = -9.486832981 Simplifying x + -30 = -9.486832981 Reorder the terms: -30 + x = -9.486832981 Solving -30 + x = -9.486832981 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 = -9.486832981 + 30 Combine like terms: -30 + 30 = 0 0 + x = -9.486832981 + 30 x = -9.486832981 + 30 Combine like terms: -9.486832981 + 30 = 20.513167019 x = 20.513167019 Simplifying x = 20.513167019Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.486832981, 20.513167019}
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