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Simplifying x2 + -60x + 75 = 0 Reorder the terms: 75 + -60x + x2 = 0 Solving 75 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + -60x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -60x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -60x + x2 = 0 + -75 -60x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -60x + x2 = -75 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 = -75 + 900 Reorder the terms: 900 + -60x + x2 = -75 + 900 Combine like terms: -75 + 900 = 825 900 + -60x + x2 = 825 Factor a perfect square on the left side: (x + -30)(x + -30) = 825 Calculate the square root of the right side: 28.722813233 Break this problem into two subproblems by setting (x + -30) equal to 28.722813233 and -28.722813233.Subproblem 1
x + -30 = 28.722813233 Simplifying x + -30 = 28.722813233 Reorder the terms: -30 + x = 28.722813233 Solving -30 + x = 28.722813233 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 = 28.722813233 + 30 Combine like terms: -30 + 30 = 0 0 + x = 28.722813233 + 30 x = 28.722813233 + 30 Combine like terms: 28.722813233 + 30 = 58.722813233 x = 58.722813233 Simplifying x = 58.722813233Subproblem 2
x + -30 = -28.722813233 Simplifying x + -30 = -28.722813233 Reorder the terms: -30 + x = -28.722813233 Solving -30 + x = -28.722813233 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 = -28.722813233 + 30 Combine like terms: -30 + 30 = 0 0 + x = -28.722813233 + 30 x = -28.722813233 + 30 Combine like terms: -28.722813233 + 30 = 1.277186767 x = 1.277186767 Simplifying x = 1.277186767Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.722813233, 1.277186767}
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