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Simplifying x2 + -480x + -4000 = 0 Reorder the terms: -4000 + -480x + x2 = 0 Solving -4000 + -480x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4000' to each side of the equation. -4000 + -480x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + -480x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + -480x + x2 = 0 + 4000 -480x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 -480x + x2 = 4000 The x term is -480x. Take half its coefficient (-240). Square it (57600) and add it to both sides. Add '57600' to each side of the equation. -480x + 57600 + x2 = 4000 + 57600 Reorder the terms: 57600 + -480x + x2 = 4000 + 57600 Combine like terms: 4000 + 57600 = 61600 57600 + -480x + x2 = 61600 Factor a perfect square on the left side: (x + -240)(x + -240) = 61600 Calculate the square root of the right side: 248.19347292 Break this problem into two subproblems by setting (x + -240) equal to 248.19347292 and -248.19347292.Subproblem 1
x + -240 = 248.19347292 Simplifying x + -240 = 248.19347292 Reorder the terms: -240 + x = 248.19347292 Solving -240 + x = 248.19347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '240' to each side of the equation. -240 + 240 + x = 248.19347292 + 240 Combine like terms: -240 + 240 = 0 0 + x = 248.19347292 + 240 x = 248.19347292 + 240 Combine like terms: 248.19347292 + 240 = 488.19347292 x = 488.19347292 Simplifying x = 488.19347292Subproblem 2
x + -240 = -248.19347292 Simplifying x + -240 = -248.19347292 Reorder the terms: -240 + x = -248.19347292 Solving -240 + x = -248.19347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '240' to each side of the equation. -240 + 240 + x = -248.19347292 + 240 Combine like terms: -240 + 240 = 0 0 + x = -248.19347292 + 240 x = -248.19347292 + 240 Combine like terms: -248.19347292 + 240 = -8.19347292 x = -8.19347292 Simplifying x = -8.19347292Solution
The solution to the problem is based on the solutions from the subproblems. x = {488.19347292, -8.19347292}
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