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Simplifying x2 + -8x + -600 = 0 Reorder the terms: -600 + -8x + x2 = 0 Solving -600 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + -8x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -8x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -8x + x2 = 0 + 600 -8x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -8x + x2 = 600 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 = 600 + 16 Reorder the terms: 16 + -8x + x2 = 600 + 16 Combine like terms: 600 + 16 = 616 16 + -8x + x2 = 616 Factor a perfect square on the left side: (x + -4)(x + -4) = 616 Calculate the square root of the right side: 24.819347292 Break this problem into two subproblems by setting (x + -4) equal to 24.819347292 and -24.819347292.Subproblem 1
x + -4 = 24.819347292 Simplifying x + -4 = 24.819347292 Reorder the terms: -4 + x = 24.819347292 Solving -4 + x = 24.819347292 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 = 24.819347292 + 4 Combine like terms: -4 + 4 = 0 0 + x = 24.819347292 + 4 x = 24.819347292 + 4 Combine like terms: 24.819347292 + 4 = 28.819347292 x = 28.819347292 Simplifying x = 28.819347292Subproblem 2
x + -4 = -24.819347292 Simplifying x + -4 = -24.819347292 Reorder the terms: -4 + x = -24.819347292 Solving -4 + x = -24.819347292 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 = -24.819347292 + 4 Combine like terms: -4 + 4 = 0 0 + x = -24.819347292 + 4 x = -24.819347292 + 4 Combine like terms: -24.819347292 + 4 = -20.819347292 x = -20.819347292 Simplifying x = -20.819347292Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.819347292, -20.819347292}
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