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Simplifying x2 + 10x = 230 Reorder the terms: 10x + x2 = 230 Solving 10x + x2 = 230 Solving for variable 'x'. Reorder the terms: -230 + 10x + x2 = 230 + -230 Combine like terms: 230 + -230 = 0 -230 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '230' to each side of the equation. -230 + 10x + 230 + x2 = 0 + 230 Reorder the terms: -230 + 230 + 10x + x2 = 0 + 230 Combine like terms: -230 + 230 = 0 0 + 10x + x2 = 0 + 230 10x + x2 = 0 + 230 Combine like terms: 0 + 230 = 230 10x + x2 = 230 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 = 230 + 25 Reorder the terms: 25 + 10x + x2 = 230 + 25 Combine like terms: 230 + 25 = 255 25 + 10x + x2 = 255 Factor a perfect square on the left side: (x + 5)(x + 5) = 255 Calculate the square root of the right side: 15.968719423 Break this problem into two subproblems by setting (x + 5) equal to 15.968719423 and -15.968719423.Subproblem 1
x + 5 = 15.968719423 Simplifying x + 5 = 15.968719423 Reorder the terms: 5 + x = 15.968719423 Solving 5 + x = 15.968719423 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 = 15.968719423 + -5 Combine like terms: 5 + -5 = 0 0 + x = 15.968719423 + -5 x = 15.968719423 + -5 Combine like terms: 15.968719423 + -5 = 10.968719423 x = 10.968719423 Simplifying x = 10.968719423Subproblem 2
x + 5 = -15.968719423 Simplifying x + 5 = -15.968719423 Reorder the terms: 5 + x = -15.968719423 Solving 5 + x = -15.968719423 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 = -15.968719423 + -5 Combine like terms: 5 + -5 = 0 0 + x = -15.968719423 + -5 x = -15.968719423 + -5 Combine like terms: -15.968719423 + -5 = -20.968719423 x = -20.968719423 Simplifying x = -20.968719423Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.968719423, -20.968719423}
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