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Simplifying 0 = X2 + -1X + -7 Reorder the terms: 0 = -7 + -1X + X2 Solving 0 = -7 + -1X + X2 Solving for variable 'X'. Combine like terms: 0 + 7 = 7 7 + X + -1X2 = -7 + -1X + X2 + 7 + X + -1X2 Reorder the terms: 7 + X + -1X2 = -7 + 7 + -1X + X + X2 + -1X2 Combine like terms: -7 + 7 = 0 7 + X + -1X2 = 0 + -1X + X + X2 + -1X2 7 + X + -1X2 = -1X + X + X2 + -1X2 Combine like terms: -1X + X = 0 7 + X + -1X2 = 0 + X2 + -1X2 7 + X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 7 + X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -1X + X2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -1X + 7 + X2 = 0 + 7 Reorder the terms: -7 + 7 + -1X + X2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1X + X2 = 0 + 7 -1X + X2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1X + X2 = 7 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. -1X + 0.25 + X2 = 7 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 0.25 + -1X + X2 = 7.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (X + 0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
X + 0.5 = 2.692582404 Simplifying X + 0.5 = 2.692582404 Reorder the terms: 0.5 + X = 2.692582404 Solving 0.5 + X = 2.692582404 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 = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 2.692582404 + -0.5 X = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 X = 2.192582404 Simplifying X = 2.192582404Subproblem 2
X + 0.5 = -2.692582404 Simplifying X + 0.5 = -2.692582404 Reorder the terms: 0.5 + X = -2.692582404 Solving 0.5 + X = -2.692582404 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 = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -2.692582404 + -0.5 X = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 X = -3.192582404 Simplifying X = -3.192582404Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.192582404, -3.192582404}
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