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Simplifying X2 + X + -145 = 0 Reorder the terms: -145 + X + X2 = 0 Solving -145 + X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '145' to each side of the equation. -145 + X + 145 + X2 = 0 + 145 Reorder the terms: -145 + 145 + X + X2 = 0 + 145 Combine like terms: -145 + 145 = 0 0 + X + X2 = 0 + 145 X + X2 = 0 + 145 Combine like terms: 0 + 145 = 145 X + X2 = 145 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. X + 0.25 + X2 = 145 + 0.25 Reorder the terms: 0.25 + X + X2 = 145 + 0.25 Combine like terms: 145 + 0.25 = 145.25 0.25 + X + X2 = 145.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 145.25 Calculate the square root of the right side: 12.051970793 Break this problem into two subproblems by setting (X + 0.5) equal to 12.051970793 and -12.051970793.Subproblem 1
X + 0.5 = 12.051970793 Simplifying X + 0.5 = 12.051970793 Reorder the terms: 0.5 + X = 12.051970793 Solving 0.5 + X = 12.051970793 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 = 12.051970793 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 12.051970793 + -0.5 X = 12.051970793 + -0.5 Combine like terms: 12.051970793 + -0.5 = 11.551970793 X = 11.551970793 Simplifying X = 11.551970793Subproblem 2
X + 0.5 = -12.051970793 Simplifying X + 0.5 = -12.051970793 Reorder the terms: 0.5 + X = -12.051970793 Solving 0.5 + X = -12.051970793 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 = -12.051970793 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -12.051970793 + -0.5 X = -12.051970793 + -0.5 Combine like terms: -12.051970793 + -0.5 = -12.551970793 X = -12.551970793 Simplifying X = -12.551970793Solution
The solution to the problem is based on the solutions from the subproblems. X = {11.551970793, -12.551970793}
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