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Simplifying x2 + 8x + -300 = 1300 Reorder the terms: -300 + 8x + x2 = 1300 Solving -300 + 8x + x2 = 1300 Solving for variable 'x'. Reorder the terms: -300 + -1300 + 8x + x2 = 1300 + -1300 Combine like terms: -300 + -1300 = -1600 -1600 + 8x + x2 = 1300 + -1300 Combine like terms: 1300 + -1300 = 0 -1600 + 8x + x2 = 0 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 = 36.199502484 x = 36.199502484 Simplifying x = 36.199502484Subproblem 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 = -44.199502484 x = -44.199502484 Simplifying x = -44.199502484Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.199502484, -44.199502484}
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