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Simplifying X2 + 7X + -112 = 0 Reorder the terms: -112 + 7X + X2 = 0 Solving -112 + 7X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + 7X + 112 + X2 = 0 + 112 Reorder the terms: -112 + 112 + 7X + X2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 7X + X2 = 0 + 112 7X + X2 = 0 + 112 Combine like terms: 0 + 112 = 112 7X + X2 = 112 The X term is 7X. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7X + 12.25 + X2 = 112 + 12.25 Reorder the terms: 12.25 + 7X + X2 = 112 + 12.25 Combine like terms: 112 + 12.25 = 124.25 12.25 + 7X + X2 = 124.25 Factor a perfect square on the left side: (X + 3.5)(X + 3.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (X + 3.5) equal to 11.146748405 and -11.146748405.Subproblem 1
X + 3.5 = 11.146748405 Simplifying X + 3.5 = 11.146748405 Reorder the terms: 3.5 + X = 11.146748405 Solving 3.5 + X = 11.146748405 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = 11.146748405 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = 11.146748405 + -3.5 X = 11.146748405 + -3.5 Combine like terms: 11.146748405 + -3.5 = 7.646748405 X = 7.646748405 Simplifying X = 7.646748405Subproblem 2
X + 3.5 = -11.146748405 Simplifying X + 3.5 = -11.146748405 Reorder the terms: 3.5 + X = -11.146748405 Solving 3.5 + X = -11.146748405 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = -11.146748405 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = -11.146748405 + -3.5 X = -11.146748405 + -3.5 Combine like terms: -11.146748405 + -3.5 = -14.646748405 X = -14.646748405 Simplifying X = -14.646748405Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.646748405, -14.646748405}
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