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Simplifying X2 + 2X + -4800 = 0 Reorder the terms: -4800 + 2X + X2 = 0 Solving -4800 + 2X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '4800' to each side of the equation. -4800 + 2X + 4800 + X2 = 0 + 4800 Reorder the terms: -4800 + 4800 + 2X + X2 = 0 + 4800 Combine like terms: -4800 + 4800 = 0 0 + 2X + X2 = 0 + 4800 2X + X2 = 0 + 4800 Combine like terms: 0 + 4800 = 4800 2X + X2 = 4800 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = 4800 + 1 Reorder the terms: 1 + 2X + X2 = 4800 + 1 Combine like terms: 4800 + 1 = 4801 1 + 2X + X2 = 4801 Factor a perfect square on the left side: (X + 1)(X + 1) = 4801 Calculate the square root of the right side: 69.289248805 Break this problem into two subproblems by setting (X + 1) equal to 69.289248805 and -69.289248805.Subproblem 1
X + 1 = 69.289248805 Simplifying X + 1 = 69.289248805 Reorder the terms: 1 + X = 69.289248805 Solving 1 + X = 69.289248805 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 69.289248805 + -1 Combine like terms: 1 + -1 = 0 0 + X = 69.289248805 + -1 X = 69.289248805 + -1 Combine like terms: 69.289248805 + -1 = 68.289248805 X = 68.289248805 Simplifying X = 68.289248805Subproblem 2
X + 1 = -69.289248805 Simplifying X + 1 = -69.289248805 Reorder the terms: 1 + X = -69.289248805 Solving 1 + X = -69.289248805 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -69.289248805 + -1 Combine like terms: 1 + -1 = 0 0 + X = -69.289248805 + -1 X = -69.289248805 + -1 Combine like terms: -69.289248805 + -1 = -70.289248805 X = -70.289248805 Simplifying X = -70.289248805Solution
The solution to the problem is based on the solutions from the subproblems. X = {68.289248805, -70.289248805}
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