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Simplifying X2 + 4 = 10X Reorder the terms: 4 + X2 = 10X Solving 4 + X2 = 10X Solving for variable 'X'. Reorder the terms: 4 + -10X + X2 = 10X + -10X Combine like terms: 10X + -10X = 0 4 + -10X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10X + -4 + X2 = 0 + -4 Reorder the terms: 4 + -4 + -10X + X2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10X + X2 = 0 + -4 -10X + X2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10X + X2 = -4 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 = -4 + 25 Reorder the terms: 25 + -10X + X2 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + -10X + X2 = 21 Factor a perfect square on the left side: (X + -5)(X + -5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (X + -5) equal to 4.582575695 and -4.582575695.Subproblem 1
X + -5 = 4.582575695 Simplifying X + -5 = 4.582575695 Reorder the terms: -5 + X = 4.582575695 Solving -5 + X = 4.582575695 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 = 4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + X = 4.582575695 + 5 X = 4.582575695 + 5 Combine like terms: 4.582575695 + 5 = 9.582575695 X = 9.582575695 Simplifying X = 9.582575695Subproblem 2
X + -5 = -4.582575695 Simplifying X + -5 = -4.582575695 Reorder the terms: -5 + X = -4.582575695 Solving -5 + X = -4.582575695 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 = -4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + X = -4.582575695 + 5 X = -4.582575695 + 5 Combine like terms: -4.582575695 + 5 = 0.417424305 X = 0.417424305 Simplifying X = 0.417424305Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.582575695, 0.417424305}
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