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Simplifying 4 = X2 + X Reorder the terms: 4 = X + X2 Solving 4 = X + X2 Solving for variable 'X'. Reorder the terms: 4 + -1X + -1X2 = X + -1X + X2 + -1X2 Combine like terms: X + -1X = 0 4 + -1X + -1X2 = 0 + X2 + -1X2 4 + -1X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 4 + -1X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + X + X2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + X + 4 + X2 = 0 + 4 Reorder the terms: -4 + 4 + X + X2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + X + X2 = 0 + 4 X + X2 = 0 + 4 Combine like terms: 0 + 4 = 4 X + X2 = 4 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + X2 = 4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + X2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 1.25 + X2 = 4.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (X + 0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
X + 0.5 = 2.061552813 Simplifying X + 0.5 = 2.061552813 Reorder the terms: 0.5 + X = 2.061552813 Solving 0.5 + X = 2.061552813 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 2.061552813 + -0.5 X = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 X = 1.561552813 Simplifying X = 1.561552813Subproblem 2
X + 0.5 = -2.061552813 Simplifying X + 0.5 = -2.061552813 Reorder the terms: 0.5 + X = -2.061552813 Solving 0.5 + X = -2.061552813 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -2.061552813 + -0.5 X = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 X = -2.561552813 Simplifying X = -2.561552813Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.561552813, -2.561552813}
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