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Simplifying X2 + 10X + -800 = 0 Reorder the terms: -800 + 10X + X2 = 0 Solving -800 + 10X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + 10X + 800 + X2 = 0 + 800 Reorder the terms: -800 + 800 + 10X + X2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 10X + X2 = 0 + 800 10X + X2 = 0 + 800 Combine like terms: 0 + 800 = 800 10X + X2 = 800 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 = 800 + 25 Reorder the terms: 25 + 10X + X2 = 800 + 25 Combine like terms: 800 + 25 = 825 25 + 10X + X2 = 825 Factor a perfect square on the left side: (X + 5)(X + 5) = 825 Calculate the square root of the right side: 28.722813233 Break this problem into two subproblems by setting (X + 5) equal to 28.722813233 and -28.722813233.Subproblem 1
X + 5 = 28.722813233 Simplifying X + 5 = 28.722813233 Reorder the terms: 5 + X = 28.722813233 Solving 5 + X = 28.722813233 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 = 28.722813233 + -5 Combine like terms: 5 + -5 = 0 0 + X = 28.722813233 + -5 X = 28.722813233 + -5 Combine like terms: 28.722813233 + -5 = 23.722813233 X = 23.722813233 Simplifying X = 23.722813233Subproblem 2
X + 5 = -28.722813233 Simplifying X + 5 = -28.722813233 Reorder the terms: 5 + X = -28.722813233 Solving 5 + X = -28.722813233 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 = -28.722813233 + -5 Combine like terms: 5 + -5 = 0 0 + X = -28.722813233 + -5 X = -28.722813233 + -5 Combine like terms: -28.722813233 + -5 = -33.722813233 X = -33.722813233 Simplifying X = -33.722813233Solution
The solution to the problem is based on the solutions from the subproblems. X = {23.722813233, -33.722813233}
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