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Simplifying x2 + 5x + -1600 = 0 Reorder the terms: -1600 + 5x + x2 = 0 Solving -1600 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 5x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 5x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 5x + x2 = 0 + 1600 5x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 5x + x2 = 1600 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1600 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1600 + 6.25 Combine like terms: 1600 + 6.25 = 1606.25 6.25 + 5x + x2 = 1606.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1606.25 Calculate the square root of the right side: 40.078048855 Break this problem into two subproblems by setting (x + 2.5) equal to 40.078048855 and -40.078048855.Subproblem 1
x + 2.5 = 40.078048855 Simplifying x + 2.5 = 40.078048855 Reorder the terms: 2.5 + x = 40.078048855 Solving 2.5 + x = 40.078048855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 40.078048855 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 40.078048855 + -2.5 x = 40.078048855 + -2.5 Combine like terms: 40.078048855 + -2.5 = 37.578048855 x = 37.578048855 Simplifying x = 37.578048855Subproblem 2
x + 2.5 = -40.078048855 Simplifying x + 2.5 = -40.078048855 Reorder the terms: 2.5 + x = -40.078048855 Solving 2.5 + x = -40.078048855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -40.078048855 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -40.078048855 + -2.5 x = -40.078048855 + -2.5 Combine like terms: -40.078048855 + -2.5 = -42.578048855 x = -42.578048855 Simplifying x = -42.578048855Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.578048855, -42.578048855}
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