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Simplifying x2 + -8x + -1600 = 0 Reorder the terms: -1600 + -8x + x2 = 0 Solving -1600 + -8x + 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 + -8x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + -8x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + -8x + x2 = 0 + 1600 -8x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 -8x + x2 = 1600 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 1600 + 16 Reorder the terms: 16 + -8x + x2 = 1600 + 16 Combine like terms: 1600 + 16 = 1616 16 + -8x + x2 = 1616 Factor a perfect square on the left side: (x + -4)(x + -4) = 1616 Calculate the square root of the right side: 40.199502484 Break this problem into two subproblems by setting (x + -4) equal to 40.199502484 and -40.199502484.Subproblem 1
x + -4 = 40.199502484 Simplifying x + -4 = 40.199502484 Reorder the terms: -4 + x = 40.199502484 Solving -4 + x = 40.199502484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 40.199502484 + 4 Combine like terms: -4 + 4 = 0 0 + x = 40.199502484 + 4 x = 40.199502484 + 4 Combine like terms: 40.199502484 + 4 = 44.199502484 x = 44.199502484 Simplifying x = 44.199502484Subproblem 2
x + -4 = -40.199502484 Simplifying x + -4 = -40.199502484 Reorder the terms: -4 + x = -40.199502484 Solving -4 + x = -40.199502484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -40.199502484 + 4 Combine like terms: -4 + 4 = 0 0 + x = -40.199502484 + 4 x = -40.199502484 + 4 Combine like terms: -40.199502484 + 4 = -36.199502484 x = -36.199502484 Simplifying x = -36.199502484Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.199502484, -36.199502484}
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