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Simplifying x2 + -7x + -90 = 0 Reorder the terms: -90 + -7x + x2 = 0 Solving -90 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -7x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -7x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -7x + x2 = 0 + 90 -7x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -7x + x2 = 90 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 = 90 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 90 + 12.25 Combine like terms: 90 + 12.25 = 102.25 12.25 + -7x + x2 = 102.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (x + -3.5) equal to 10.111874208 and -10.111874208.Subproblem 1
x + -3.5 = 10.111874208 Simplifying x + -3.5 = 10.111874208 Reorder the terms: -3.5 + x = 10.111874208 Solving -3.5 + x = 10.111874208 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 = 10.111874208 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 10.111874208 + 3.5 x = 10.111874208 + 3.5 Combine like terms: 10.111874208 + 3.5 = 13.611874208 x = 13.611874208 Simplifying x = 13.611874208Subproblem 2
x + -3.5 = -10.111874208 Simplifying x + -3.5 = -10.111874208 Reorder the terms: -3.5 + x = -10.111874208 Solving -3.5 + x = -10.111874208 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 = -10.111874208 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -10.111874208 + 3.5 x = -10.111874208 + 3.5 Combine like terms: -10.111874208 + 3.5 = -6.611874208 x = -6.611874208 Simplifying x = -6.611874208Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.611874208, -6.611874208}
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