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Simplifying (X + 64)(X + -14) = 23 Reorder the terms: (64 + X)(X + -14) = 23 Reorder the terms: (64 + X)(-14 + X) = 23 Multiply (64 + X) * (-14 + X) (64(-14 + X) + X(-14 + X)) = 23 ((-14 * 64 + X * 64) + X(-14 + X)) = 23 ((-896 + 64X) + X(-14 + X)) = 23 (-896 + 64X + (-14 * X + X * X)) = 23 (-896 + 64X + (-14X + X2)) = 23 Combine like terms: 64X + -14X = 50X (-896 + 50X + X2) = 23 Solving -896 + 50X + X2 = 23 Solving for variable 'X'. Reorder the terms: -896 + -23 + 50X + X2 = 23 + -23 Combine like terms: -896 + -23 = -919 -919 + 50X + X2 = 23 + -23 Combine like terms: 23 + -23 = 0 -919 + 50X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '919' to each side of the equation. -919 + 50X + 919 + X2 = 0 + 919 Reorder the terms: -919 + 919 + 50X + X2 = 0 + 919 Combine like terms: -919 + 919 = 0 0 + 50X + X2 = 0 + 919 50X + X2 = 0 + 919 Combine like terms: 0 + 919 = 919 50X + X2 = 919 The X term is 50X. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50X + 625 + X2 = 919 + 625 Reorder the terms: 625 + 50X + X2 = 919 + 625 Combine like terms: 919 + 625 = 1544 625 + 50X + X2 = 1544 Factor a perfect square on the left side: (X + 25)(X + 25) = 1544 Calculate the square root of the right side: 39.293765409 Break this problem into two subproblems by setting (X + 25) equal to 39.293765409 and -39.293765409.Subproblem 1
X + 25 = 39.293765409 Simplifying X + 25 = 39.293765409 Reorder the terms: 25 + X = 39.293765409 Solving 25 + X = 39.293765409 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + X = 39.293765409 + -25 Combine like terms: 25 + -25 = 0 0 + X = 39.293765409 + -25 X = 39.293765409 + -25 Combine like terms: 39.293765409 + -25 = 14.293765409 X = 14.293765409 Simplifying X = 14.293765409Subproblem 2
X + 25 = -39.293765409 Simplifying X + 25 = -39.293765409 Reorder the terms: 25 + X = -39.293765409 Solving 25 + X = -39.293765409 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + X = -39.293765409 + -25 Combine like terms: 25 + -25 = 0 0 + X = -39.293765409 + -25 X = -39.293765409 + -25 Combine like terms: -39.293765409 + -25 = -64.293765409 X = -64.293765409 Simplifying X = -64.293765409Solution
The solution to the problem is based on the solutions from the subproblems. X = {14.293765409, -64.293765409}
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