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Simplifying x2 + 10x + -872 = 0 Reorder the terms: -872 + 10x + x2 = 0 Solving -872 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '872' to each side of the equation. -872 + 10x + 872 + x2 = 0 + 872 Reorder the terms: -872 + 872 + 10x + x2 = 0 + 872 Combine like terms: -872 + 872 = 0 0 + 10x + x2 = 0 + 872 10x + x2 = 0 + 872 Combine like terms: 0 + 872 = 872 10x + x2 = 872 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 872 + 25 Reorder the terms: 25 + 10x + x2 = 872 + 25 Combine like terms: 872 + 25 = 897 25 + 10x + x2 = 897 Factor a perfect square on the left side: (x + 5)(x + 5) = 897 Calculate the square root of the right side: 29.949958264 Break this problem into two subproblems by setting (x + 5) equal to 29.949958264 and -29.949958264.Subproblem 1
x + 5 = 29.949958264 Simplifying x + 5 = 29.949958264 Reorder the terms: 5 + x = 29.949958264 Solving 5 + x = 29.949958264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 29.949958264 + -5 Combine like terms: 5 + -5 = 0 0 + x = 29.949958264 + -5 x = 29.949958264 + -5 Combine like terms: 29.949958264 + -5 = 24.949958264 x = 24.949958264 Simplifying x = 24.949958264Subproblem 2
x + 5 = -29.949958264 Simplifying x + 5 = -29.949958264 Reorder the terms: 5 + x = -29.949958264 Solving 5 + x = -29.949958264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -29.949958264 + -5 Combine like terms: 5 + -5 = 0 0 + x = -29.949958264 + -5 x = -29.949958264 + -5 Combine like terms: -29.949958264 + -5 = -34.949958264 x = -34.949958264 Simplifying x = -34.949958264Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.949958264, -34.949958264}
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