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Simplifying x2 + -72x + 100 = 0 Reorder the terms: 100 + -72x + x2 = 0 Solving 100 + -72x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -72x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -72x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -72x + x2 = 0 + -100 -72x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -72x + x2 = -100 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = -100 + 1296 Reorder the terms: 1296 + -72x + x2 = -100 + 1296 Combine like terms: -100 + 1296 = 1196 1296 + -72x + x2 = 1196 Factor a perfect square on the left side: (x + -36)(x + -36) = 1196 Calculate the square root of the right side: 34.583232932 Break this problem into two subproblems by setting (x + -36) equal to 34.583232932 and -34.583232932.Subproblem 1
x + -36 = 34.583232932 Simplifying x + -36 = 34.583232932 Reorder the terms: -36 + x = 34.583232932 Solving -36 + x = 34.583232932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 34.583232932 + 36 Combine like terms: -36 + 36 = 0 0 + x = 34.583232932 + 36 x = 34.583232932 + 36 Combine like terms: 34.583232932 + 36 = 70.583232932 x = 70.583232932 Simplifying x = 70.583232932Subproblem 2
x + -36 = -34.583232932 Simplifying x + -36 = -34.583232932 Reorder the terms: -36 + x = -34.583232932 Solving -36 + x = -34.583232932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -34.583232932 + 36 Combine like terms: -36 + 36 = 0 0 + x = -34.583232932 + 36 x = -34.583232932 + 36 Combine like terms: -34.583232932 + 36 = 1.416767068 x = 1.416767068 Simplifying x = 1.416767068Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.583232932, 1.416767068}
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