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Simplifying x2 + 100x + 800 = 0 Reorder the terms: 800 + 100x + x2 = 0 Solving 800 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-800' to each side of the equation. 800 + 100x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + 100x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + 100x + x2 = 0 + -800 100x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 100x + x2 = -800 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = -800 + 2500 Reorder the terms: 2500 + 100x + x2 = -800 + 2500 Combine like terms: -800 + 2500 = 1700 2500 + 100x + x2 = 1700 Factor a perfect square on the left side: (x + 50)(x + 50) = 1700 Calculate the square root of the right side: 41.231056256 Break this problem into two subproblems by setting (x + 50) equal to 41.231056256 and -41.231056256.Subproblem 1
x + 50 = 41.231056256 Simplifying x + 50 = 41.231056256 Reorder the terms: 50 + x = 41.231056256 Solving 50 + x = 41.231056256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 41.231056256 + -50 Combine like terms: 50 + -50 = 0 0 + x = 41.231056256 + -50 x = 41.231056256 + -50 Combine like terms: 41.231056256 + -50 = -8.768943744 x = -8.768943744 Simplifying x = -8.768943744Subproblem 2
x + 50 = -41.231056256 Simplifying x + 50 = -41.231056256 Reorder the terms: 50 + x = -41.231056256 Solving 50 + x = -41.231056256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -41.231056256 + -50 Combine like terms: 50 + -50 = 0 0 + x = -41.231056256 + -50 x = -41.231056256 + -50 Combine like terms: -41.231056256 + -50 = -91.231056256 x = -91.231056256 Simplifying x = -91.231056256Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.768943744, -91.231056256}
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