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Simplifying x2 + 7x + -1260 = 0 Reorder the terms: -1260 + 7x + x2 = 0 Solving -1260 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1260' to each side of the equation. -1260 + 7x + 1260 + x2 = 0 + 1260 Reorder the terms: -1260 + 1260 + 7x + x2 = 0 + 1260 Combine like terms: -1260 + 1260 = 0 0 + 7x + x2 = 0 + 1260 7x + x2 = 0 + 1260 Combine like terms: 0 + 1260 = 1260 7x + x2 = 1260 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 = 1260 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 1260 + 12.25 Combine like terms: 1260 + 12.25 = 1272.25 12.25 + 7x + x2 = 1272.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 1272.25 Calculate the square root of the right side: 35.668613654 Break this problem into two subproblems by setting (x + 3.5) equal to 35.668613654 and -35.668613654.Subproblem 1
x + 3.5 = 35.668613654 Simplifying x + 3.5 = 35.668613654 Reorder the terms: 3.5 + x = 35.668613654 Solving 3.5 + x = 35.668613654 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 = 35.668613654 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 35.668613654 + -3.5 x = 35.668613654 + -3.5 Combine like terms: 35.668613654 + -3.5 = 32.168613654 x = 32.168613654 Simplifying x = 32.168613654Subproblem 2
x + 3.5 = -35.668613654 Simplifying x + 3.5 = -35.668613654 Reorder the terms: 3.5 + x = -35.668613654 Solving 3.5 + x = -35.668613654 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 = -35.668613654 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -35.668613654 + -3.5 x = -35.668613654 + -3.5 Combine like terms: -35.668613654 + -3.5 = -39.168613654 x = -39.168613654 Simplifying x = -39.168613654Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.168613654, -39.168613654}
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