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Simplifying x(x + 10) = 72 Reorder the terms: x(10 + x) = 72 (10 * x + x * x) = 72 (10x + x2) = 72 Solving 10x + x2 = 72 Solving for variable 'x'. Reorder the terms: -72 + 10x + x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 10x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 10x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 10x + x2 = 0 + 72 10x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 10x + x2 = 72 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 72 + 25 Reorder the terms: 25 + 10x + x2 = 72 + 25 Combine like terms: 72 + 25 = 97 25 + 10x + x2 = 97 Factor a perfect square on the left side: (x + 5)(x + 5) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + 5) equal to 9.848857802 and -9.848857802.Subproblem 1
x + 5 = 9.848857802 Simplifying x + 5 = 9.848857802 Reorder the terms: 5 + x = 9.848857802 Solving 5 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 9.848857802 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.848857802 + -5 x = 9.848857802 + -5 Combine like terms: 9.848857802 + -5 = 4.848857802 x = 4.848857802 Simplifying x = 4.848857802Subproblem 2
x + 5 = -9.848857802 Simplifying x + 5 = -9.848857802 Reorder the terms: 5 + x = -9.848857802 Solving 5 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -9.848857802 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.848857802 + -5 x = -9.848857802 + -5 Combine like terms: -9.848857802 + -5 = -14.848857802 x = -14.848857802 Simplifying x = -14.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.848857802, -14.848857802}
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