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Simplifying x2 + -7x + -1000 = 0 Reorder the terms: -1000 + -7x + x2 = 0 Solving -1000 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -7x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -7x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -7x + x2 = 0 + 1000 -7x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -7x + x2 = 1000 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 = 1000 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 1000 + 12.25 Combine like terms: 1000 + 12.25 = 1012.25 12.25 + -7x + x2 = 1012.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1012.25 Calculate the square root of the right side: 31.81587654 Break this problem into two subproblems by setting (x + -3.5) equal to 31.81587654 and -31.81587654.Subproblem 1
x + -3.5 = 31.81587654 Simplifying x + -3.5 = 31.81587654 Reorder the terms: -3.5 + x = 31.81587654 Solving -3.5 + x = 31.81587654 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 = 31.81587654 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 31.81587654 + 3.5 x = 31.81587654 + 3.5 Combine like terms: 31.81587654 + 3.5 = 35.31587654 x = 35.31587654 Simplifying x = 35.31587654Subproblem 2
x + -3.5 = -31.81587654 Simplifying x + -3.5 = -31.81587654 Reorder the terms: -3.5 + x = -31.81587654 Solving -3.5 + x = -31.81587654 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 = -31.81587654 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -31.81587654 + 3.5 x = -31.81587654 + 3.5 Combine like terms: -31.81587654 + 3.5 = -28.31587654 x = -28.31587654 Simplifying x = -28.31587654Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.31587654, -28.31587654}
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