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Simplifying 1x2 + 8x + -325 = 0 Reorder the terms: -325 + 8x + 1x2 = 0 Solving -325 + 8x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '325' to each side of the equation. -325 + 8x + 325 + x2 = 0 + 325 Reorder the terms: -325 + 325 + 8x + x2 = 0 + 325 Combine like terms: -325 + 325 = 0 0 + 8x + x2 = 0 + 325 8x + x2 = 0 + 325 Combine like terms: 0 + 325 = 325 8x + x2 = 325 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 = 325 + 16 Reorder the terms: 16 + 8x + x2 = 325 + 16 Combine like terms: 325 + 16 = 341 16 + 8x + x2 = 341 Factor a perfect square on the left side: (x + 4)(x + 4) = 341 Calculate the square root of the right side: 18.466185313 Break this problem into two subproblems by setting (x + 4) equal to 18.466185313 and -18.466185313.Subproblem 1
x + 4 = 18.466185313 Simplifying x + 4 = 18.466185313 Reorder the terms: 4 + x = 18.466185313 Solving 4 + x = 18.466185313 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 = 18.466185313 + -4 Combine like terms: 4 + -4 = 0 0 + x = 18.466185313 + -4 x = 18.466185313 + -4 Combine like terms: 18.466185313 + -4 = 14.466185313 x = 14.466185313 Simplifying x = 14.466185313Subproblem 2
x + 4 = -18.466185313 Simplifying x + 4 = -18.466185313 Reorder the terms: 4 + x = -18.466185313 Solving 4 + x = -18.466185313 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 = -18.466185313 + -4 Combine like terms: 4 + -4 = 0 0 + x = -18.466185313 + -4 x = -18.466185313 + -4 Combine like terms: -18.466185313 + -4 = -22.466185313 x = -22.466185313 Simplifying x = -22.466185313Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.466185313, -22.466185313}
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