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Simplifying x(x + -72) + 8 = 0 Reorder the terms: x(-72 + x) + 8 = 0 (-72 * x + x * x) + 8 = 0 (-72x + x2) + 8 = 0 Reorder the terms: 8 + -72x + x2 = 0 Solving 8 + -72x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -72x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -72x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -72x + x2 = 0 + -8 -72x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -72x + x2 = -8 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 = -8 + 1296 Reorder the terms: 1296 + -72x + x2 = -8 + 1296 Combine like terms: -8 + 1296 = 1288 1296 + -72x + x2 = 1288 Factor a perfect square on the left side: (x + -36)(x + -36) = 1288 Calculate the square root of the right side: 35.88871689 Break this problem into two subproblems by setting (x + -36) equal to 35.88871689 and -35.88871689.Subproblem 1
x + -36 = 35.88871689 Simplifying x + -36 = 35.88871689 Reorder the terms: -36 + x = 35.88871689 Solving -36 + x = 35.88871689 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 = 35.88871689 + 36 Combine like terms: -36 + 36 = 0 0 + x = 35.88871689 + 36 x = 35.88871689 + 36 Combine like terms: 35.88871689 + 36 = 71.88871689 x = 71.88871689 Simplifying x = 71.88871689Subproblem 2
x + -36 = -35.88871689 Simplifying x + -36 = -35.88871689 Reorder the terms: -36 + x = -35.88871689 Solving -36 + x = -35.88871689 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 = -35.88871689 + 36 Combine like terms: -36 + 36 = 0 0 + x = -35.88871689 + 36 x = -35.88871689 + 36 Combine like terms: -35.88871689 + 36 = 0.11128311 x = 0.11128311 Simplifying x = 0.11128311Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.88871689, 0.11128311}
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