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Simplifying x2 + 10x = 1008 Reorder the terms: 10x + x2 = 1008 Solving 10x + x2 = 1008 Solving for variable 'x'. Reorder the terms: -1008 + 10x + x2 = 1008 + -1008 Combine like terms: 1008 + -1008 = 0 -1008 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1008' to each side of the equation. -1008 + 10x + 1008 + x2 = 0 + 1008 Reorder the terms: -1008 + 1008 + 10x + x2 = 0 + 1008 Combine like terms: -1008 + 1008 = 0 0 + 10x + x2 = 0 + 1008 10x + x2 = 0 + 1008 Combine like terms: 0 + 1008 = 1008 10x + x2 = 1008 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 = 1008 + 25 Reorder the terms: 25 + 10x + x2 = 1008 + 25 Combine like terms: 1008 + 25 = 1033 25 + 10x + x2 = 1033 Factor a perfect square on the left side: (x + 5)(x + 5) = 1033 Calculate the square root of the right side: 32.14031736 Break this problem into two subproblems by setting (x + 5) equal to 32.14031736 and -32.14031736.Subproblem 1
x + 5 = 32.14031736 Simplifying x + 5 = 32.14031736 Reorder the terms: 5 + x = 32.14031736 Solving 5 + x = 32.14031736 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 = 32.14031736 + -5 Combine like terms: 5 + -5 = 0 0 + x = 32.14031736 + -5 x = 32.14031736 + -5 Combine like terms: 32.14031736 + -5 = 27.14031736 x = 27.14031736 Simplifying x = 27.14031736Subproblem 2
x + 5 = -32.14031736 Simplifying x + 5 = -32.14031736 Reorder the terms: 5 + x = -32.14031736 Solving 5 + x = -32.14031736 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 = -32.14031736 + -5 Combine like terms: 5 + -5 = 0 0 + x = -32.14031736 + -5 x = -32.14031736 + -5 Combine like terms: -32.14031736 + -5 = -37.14031736 x = -37.14031736 Simplifying x = -37.14031736Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.14031736, -37.14031736}
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