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Simplifying X2 + 10X + -3200 = 0 Reorder the terms: -3200 + 10X + X2 = 0 Solving -3200 + 10X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '3200' to each side of the equation. -3200 + 10X + 3200 + X2 = 0 + 3200 Reorder the terms: -3200 + 3200 + 10X + X2 = 0 + 3200 Combine like terms: -3200 + 3200 = 0 0 + 10X + X2 = 0 + 3200 10X + X2 = 0 + 3200 Combine like terms: 0 + 3200 = 3200 10X + X2 = 3200 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 = 3200 + 25 Reorder the terms: 25 + 10X + X2 = 3200 + 25 Combine like terms: 3200 + 25 = 3225 25 + 10X + X2 = 3225 Factor a perfect square on the left side: (X + 5)(X + 5) = 3225 Calculate the square root of the right side: 56.789083458 Break this problem into two subproblems by setting (X + 5) equal to 56.789083458 and -56.789083458.Subproblem 1
X + 5 = 56.789083458 Simplifying X + 5 = 56.789083458 Reorder the terms: 5 + X = 56.789083458 Solving 5 + X = 56.789083458 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 = 56.789083458 + -5 Combine like terms: 5 + -5 = 0 0 + X = 56.789083458 + -5 X = 56.789083458 + -5 Combine like terms: 56.789083458 + -5 = 51.789083458 X = 51.789083458 Simplifying X = 51.789083458Subproblem 2
X + 5 = -56.789083458 Simplifying X + 5 = -56.789083458 Reorder the terms: 5 + X = -56.789083458 Solving 5 + X = -56.789083458 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 = -56.789083458 + -5 Combine like terms: 5 + -5 = 0 0 + X = -56.789083458 + -5 X = -56.789083458 + -5 Combine like terms: -56.789083458 + -5 = -61.789083458 X = -61.789083458 Simplifying X = -61.789083458Solution
The solution to the problem is based on the solutions from the subproblems. X = {51.789083458, -61.789083458}
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