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Simplifying (25 + -2X) + (X2 + -8X) + (X + -15) + (X + -4) = 64 Remove parenthesis around (25 + -2X) 25 + -2X + (X2 + -8X) + (X + -15) + (X + -4) = 64 Reorder the terms: 25 + -2X + (-8X + X2) + (X + -15) + (X + -4) = 64 Remove parenthesis around (-8X + X2) 25 + -2X + -8X + X2 + (X + -15) + (X + -4) = 64 Reorder the terms: 25 + -2X + -8X + X2 + (-15 + X) + (X + -4) = 64 Remove parenthesis around (-15 + X) 25 + -2X + -8X + X2 + -15 + X + (X + -4) = 64 Reorder the terms: 25 + -2X + -8X + X2 + -15 + X + (-4 + X) = 64 Remove parenthesis around (-4 + X) 25 + -2X + -8X + X2 + -15 + X + -4 + X = 64 Reorder the terms: 25 + -15 + -4 + -2X + -8X + X + X + X2 = 64 Combine like terms: 25 + -15 = 10 10 + -4 + -2X + -8X + X + X + X2 = 64 Combine like terms: 10 + -4 = 6 6 + -2X + -8X + X + X + X2 = 64 Combine like terms: -2X + -8X = -10X 6 + -10X + X + X + X2 = 64 Combine like terms: -10X + X = -9X 6 + -9X + X + X2 = 64 Combine like terms: -9X + X = -8X 6 + -8X + X2 = 64 Solving 6 + -8X + X2 = 64 Solving for variable 'X'. Reorder the terms: 6 + -64 + -8X + X2 = 64 + -64 Combine like terms: 6 + -64 = -58 -58 + -8X + X2 = 64 + -64 Combine like terms: 64 + -64 = 0 -58 + -8X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -8X + 58 + X2 = 0 + 58 Reorder the terms: -58 + 58 + -8X + X2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -8X + X2 = 0 + 58 -8X + X2 = 0 + 58 Combine like terms: 0 + 58 = 58 -8X + X2 = 58 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 = 58 + 16 Reorder the terms: 16 + -8X + X2 = 58 + 16 Combine like terms: 58 + 16 = 74 16 + -8X + X2 = 74 Factor a perfect square on the left side: (X + -4)(X + -4) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (X + -4) equal to 8.602325267 and -8.602325267.Subproblem 1
X + -4 = 8.602325267 Simplifying X + -4 = 8.602325267 Reorder the terms: -4 + X = 8.602325267 Solving -4 + X = 8.602325267 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 = 8.602325267 + 4 Combine like terms: -4 + 4 = 0 0 + X = 8.602325267 + 4 X = 8.602325267 + 4 Combine like terms: 8.602325267 + 4 = 12.602325267 X = 12.602325267 Simplifying X = 12.602325267Subproblem 2
X + -4 = -8.602325267 Simplifying X + -4 = -8.602325267 Reorder the terms: -4 + X = -8.602325267 Solving -4 + X = -8.602325267 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 = -8.602325267 + 4 Combine like terms: -4 + 4 = 0 0 + X = -8.602325267 + 4 X = -8.602325267 + 4 Combine like terms: -8.602325267 + 4 = -4.602325267 X = -4.602325267 Simplifying X = -4.602325267Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.602325267, -4.602325267}
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