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Simplifying X2 + 10 = 10X Reorder the terms: 10 + X2 = 10X Solving 10 + X2 = 10X Solving for variable 'X'. Reorder the terms: 10 + -10X + X2 = 10X + -10X Combine like terms: 10X + -10X = 0 10 + -10X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -10X + -10 + X2 = 0 + -10 Reorder the terms: 10 + -10 + -10X + X2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -10X + X2 = 0 + -10 -10X + X2 = 0 + -10 Combine like terms: 0 + -10 = -10 -10X + X2 = -10 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 = -10 + 25 Reorder the terms: 25 + -10X + X2 = -10 + 25 Combine like terms: -10 + 25 = 15 25 + -10X + X2 = 15 Factor a perfect square on the left side: (X + -5)(X + -5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (X + -5) equal to 3.872983346 and -3.872983346.Subproblem 1
X + -5 = 3.872983346 Simplifying X + -5 = 3.872983346 Reorder the terms: -5 + X = 3.872983346 Solving -5 + X = 3.872983346 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 = 3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + X = 3.872983346 + 5 X = 3.872983346 + 5 Combine like terms: 3.872983346 + 5 = 8.872983346 X = 8.872983346 Simplifying X = 8.872983346Subproblem 2
X + -5 = -3.872983346 Simplifying X + -5 = -3.872983346 Reorder the terms: -5 + X = -3.872983346 Solving -5 + X = -3.872983346 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 = -3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + X = -3.872983346 + 5 X = -3.872983346 + 5 Combine like terms: -3.872983346 + 5 = 1.127016654 X = 1.127016654 Simplifying X = 1.127016654Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.872983346, 1.127016654}
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