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Simplifying x2 + -60x + 200 = 0 Reorder the terms: 200 + -60x + x2 = 0 Solving 200 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -60x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -60x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -60x + x2 = 0 + -200 -60x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -60x + x2 = -200 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 = -200 + 900 Reorder the terms: 900 + -60x + x2 = -200 + 900 Combine like terms: -200 + 900 = 700 900 + -60x + x2 = 700 Factor a perfect square on the left side: (x + -30)(x + -30) = 700 Calculate the square root of the right side: 26.457513111 Break this problem into two subproblems by setting (x + -30) equal to 26.457513111 and -26.457513111.Subproblem 1
x + -30 = 26.457513111 Simplifying x + -30 = 26.457513111 Reorder the terms: -30 + x = 26.457513111 Solving -30 + x = 26.457513111 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 = 26.457513111 + 30 Combine like terms: -30 + 30 = 0 0 + x = 26.457513111 + 30 x = 26.457513111 + 30 Combine like terms: 26.457513111 + 30 = 56.457513111 x = 56.457513111 Simplifying x = 56.457513111Subproblem 2
x + -30 = -26.457513111 Simplifying x + -30 = -26.457513111 Reorder the terms: -30 + x = -26.457513111 Solving -30 + x = -26.457513111 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 = -26.457513111 + 30 Combine like terms: -30 + 30 = 0 0 + x = -26.457513111 + 30 x = -26.457513111 + 30 Combine like terms: -26.457513111 + 30 = 3.542486889 x = 3.542486889 Simplifying x = 3.542486889Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.457513111, 3.542486889}
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