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Simplifying 4x2 + -1y2 + 16z2 + -4z + 64 = 100 Reorder the terms: 64 + 4x2 + -1y2 + -4z + 16z2 = 100 Solving 64 + 4x2 + -1y2 + -4z + 16z2 = 100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + 4x2 + -1y2 + -4z + -64 + 16z2 = 100 + -64 Reorder the terms: 64 + -64 + 4x2 + -1y2 + -4z + 16z2 = 100 + -64 Combine like terms: 64 + -64 = 0 0 + 4x2 + -1y2 + -4z + 16z2 = 100 + -64 4x2 + -1y2 + -4z + 16z2 = 100 + -64 Combine like terms: 100 + -64 = 36 4x2 + -1y2 + -4z + 16z2 = 36 Add 'y2' to each side of the equation. 4x2 + -1y2 + -4z + y2 + 16z2 = 36 + y2 Reorder the terms: 4x2 + -1y2 + y2 + -4z + 16z2 = 36 + y2 Combine like terms: -1y2 + y2 = 0 4x2 + 0 + -4z + 16z2 = 36 + y2 4x2 + -4z + 16z2 = 36 + y2 Add '4z' to each side of the equation. 4x2 + -4z + 4z + 16z2 = 36 + y2 + 4z Combine like terms: -4z + 4z = 0 4x2 + 0 + 16z2 = 36 + y2 + 4z 4x2 + 16z2 = 36 + y2 + 4z Add '-16z2' to each side of the equation. 4x2 + 16z2 + -16z2 = 36 + y2 + 4z + -16z2 Combine like terms: 16z2 + -16z2 = 0 4x2 + 0 = 36 + y2 + 4z + -16z2 4x2 = 36 + y2 + 4z + -16z2 Divide each side by '4'. x2 = 9 + 0.25y2 + z + -4z2 Simplifying x2 = 9 + 0.25y2 + z + -4z2 Reorder the terms: -9 + x2 + -0.25y2 + -1z + 4z2 = 9 + 0.25y2 + z + -4z2 + -9 + -0.25y2 + -1z + 4z2 Reorder the terms: -9 + x2 + -0.25y2 + -1z + 4z2 = 9 + -9 + 0.25y2 + -0.25y2 + z + -1z + -4z2 + 4z2 Combine like terms: 9 + -9 = 0 -9 + x2 + -0.25y2 + -1z + 4z2 = 0 + 0.25y2 + -0.25y2 + z + -1z + -4z2 + 4z2 -9 + x2 + -0.25y2 + -1z + 4z2 = 0.25y2 + -0.25y2 + z + -1z + -4z2 + 4z2 Combine like terms: 0.25y2 + -0.25y2 = 0.00 -9 + x2 + -0.25y2 + -1z + 4z2 = 0.00 + z + -1z + -4z2 + 4z2 -9 + x2 + -0.25y2 + -1z + 4z2 = z + -1z + -4z2 + 4z2 Combine like terms: z + -1z = 0 -9 + x2 + -0.25y2 + -1z + 4z2 = 0 + -4z2 + 4z2 -9 + x2 + -0.25y2 + -1z + 4z2 = -4z2 + 4z2 Combine like terms: -4z2 + 4z2 = 0 -9 + x2 + -0.25y2 + -1z + 4z2 = 0 The solution to this equation could not be determined.
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