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Simplifying x2 + 10x + -3244 = 0 Reorder the terms: -3244 + 10x + x2 = 0 Solving -3244 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3244' to each side of the equation. -3244 + 10x + 3244 + x2 = 0 + 3244 Reorder the terms: -3244 + 3244 + 10x + x2 = 0 + 3244 Combine like terms: -3244 + 3244 = 0 0 + 10x + x2 = 0 + 3244 10x + x2 = 0 + 3244 Combine like terms: 0 + 3244 = 3244 10x + x2 = 3244 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 = 3244 + 25 Reorder the terms: 25 + 10x + x2 = 3244 + 25 Combine like terms: 3244 + 25 = 3269 25 + 10x + x2 = 3269 Factor a perfect square on the left side: (x + 5)(x + 5) = 3269 Calculate the square root of the right side: 57.175169436 Break this problem into two subproblems by setting (x + 5) equal to 57.175169436 and -57.175169436.Subproblem 1
x + 5 = 57.175169436 Simplifying x + 5 = 57.175169436 Reorder the terms: 5 + x = 57.175169436 Solving 5 + x = 57.175169436 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 = 57.175169436 + -5 Combine like terms: 5 + -5 = 0 0 + x = 57.175169436 + -5 x = 57.175169436 + -5 Combine like terms: 57.175169436 + -5 = 52.175169436 x = 52.175169436 Simplifying x = 52.175169436Subproblem 2
x + 5 = -57.175169436 Simplifying x + 5 = -57.175169436 Reorder the terms: 5 + x = -57.175169436 Solving 5 + x = -57.175169436 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 = -57.175169436 + -5 Combine like terms: 5 + -5 = 0 0 + x = -57.175169436 + -5 x = -57.175169436 + -5 Combine like terms: -57.175169436 + -5 = -62.175169436 x = -62.175169436 Simplifying x = -62.175169436Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.175169436, -62.175169436}
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