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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 = 14.646748405 x = 14.646748405 Simplifying x = 14.646748405Subproblem 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 = -7.646748405 x = -7.646748405 Simplifying x = -7.646748405Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.646748405, -7.646748405}
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