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Simplifying x2 + 20x + -8035 = 0 Reorder the terms: -8035 + 20x + x2 = 0 Solving -8035 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8035' to each side of the equation. -8035 + 20x + 8035 + x2 = 0 + 8035 Reorder the terms: -8035 + 8035 + 20x + x2 = 0 + 8035 Combine like terms: -8035 + 8035 = 0 0 + 20x + x2 = 0 + 8035 20x + x2 = 0 + 8035 Combine like terms: 0 + 8035 = 8035 20x + x2 = 8035 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 8035 + 100 Reorder the terms: 100 + 20x + x2 = 8035 + 100 Combine like terms: 8035 + 100 = 8135 100 + 20x + x2 = 8135 Factor a perfect square on the left side: (x + 10)(x + 10) = 8135 Calculate the square root of the right side: 90.194234849 Break this problem into two subproblems by setting (x + 10) equal to 90.194234849 and -90.194234849.Subproblem 1
x + 10 = 90.194234849 Simplifying x + 10 = 90.194234849 Reorder the terms: 10 + x = 90.194234849 Solving 10 + x = 90.194234849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 90.194234849 + -10 Combine like terms: 10 + -10 = 0 0 + x = 90.194234849 + -10 x = 90.194234849 + -10 Combine like terms: 90.194234849 + -10 = 80.194234849 x = 80.194234849 Simplifying x = 80.194234849Subproblem 2
x + 10 = -90.194234849 Simplifying x + 10 = -90.194234849 Reorder the terms: 10 + x = -90.194234849 Solving 10 + x = -90.194234849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -90.194234849 + -10 Combine like terms: 10 + -10 = 0 0 + x = -90.194234849 + -10 x = -90.194234849 + -10 Combine like terms: -90.194234849 + -10 = -100.194234849 x = -100.194234849 Simplifying x = -100.194234849Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.194234849, -100.194234849}
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