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Simplifying x2 + -7x + -20 = 0 Reorder the terms: -20 + -7x + x2 = 0 Solving -20 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -7x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -7x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -7x + x2 = 0 + 20 -7x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -7x + x2 = 20 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 = 20 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 20 + 12.25 Combine like terms: 20 + 12.25 = 32.25 12.25 + -7x + x2 = 32.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + -3.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + -3.5 = 5.678908346 Simplifying x + -3.5 = 5.678908346 Reorder the terms: -3.5 + x = 5.678908346 Solving -3.5 + x = 5.678908346 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 = 5.678908346 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.678908346 + 3.5 x = 5.678908346 + 3.5 Combine like terms: 5.678908346 + 3.5 = 9.178908346 x = 9.178908346 Simplifying x = 9.178908346Subproblem 2
x + -3.5 = -5.678908346 Simplifying x + -3.5 = -5.678908346 Reorder the terms: -3.5 + x = -5.678908346 Solving -3.5 + x = -5.678908346 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 = -5.678908346 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.678908346 + 3.5 x = -5.678908346 + 3.5 Combine like terms: -5.678908346 + 3.5 = -2.178908346 x = -2.178908346 Simplifying x = -2.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.178908346, -2.178908346}
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