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Simplifying x2 + 10x = 576 Reorder the terms: 10x + x2 = 576 Solving 10x + x2 = 576 Solving for variable 'x'. Reorder the terms: -576 + 10x + x2 = 576 + -576 Combine like terms: 576 + -576 = 0 -576 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + 10x + 576 + x2 = 0 + 576 Reorder the terms: -576 + 576 + 10x + x2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + 10x + x2 = 0 + 576 10x + x2 = 0 + 576 Combine like terms: 0 + 576 = 576 10x + x2 = 576 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 = 576 + 25 Reorder the terms: 25 + 10x + x2 = 576 + 25 Combine like terms: 576 + 25 = 601 25 + 10x + x2 = 601 Factor a perfect square on the left side: (x + 5)(x + 5) = 601 Calculate the square root of the right side: 24.515301344 Break this problem into two subproblems by setting (x + 5) equal to 24.515301344 and -24.515301344.Subproblem 1
x + 5 = 24.515301344 Simplifying x + 5 = 24.515301344 Reorder the terms: 5 + x = 24.515301344 Solving 5 + x = 24.515301344 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 = 24.515301344 + -5 Combine like terms: 5 + -5 = 0 0 + x = 24.515301344 + -5 x = 24.515301344 + -5 Combine like terms: 24.515301344 + -5 = 19.515301344 x = 19.515301344 Simplifying x = 19.515301344Subproblem 2
x + 5 = -24.515301344 Simplifying x + 5 = -24.515301344 Reorder the terms: 5 + x = -24.515301344 Solving 5 + x = -24.515301344 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 = -24.515301344 + -5 Combine like terms: 5 + -5 = 0 0 + x = -24.515301344 + -5 x = -24.515301344 + -5 Combine like terms: -24.515301344 + -5 = -29.515301344 x = -29.515301344 Simplifying x = -29.515301344Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.515301344, -29.515301344}
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