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Simplifying 2x2 + 2y2 + 2z2 + 4y + -2z = 100 Reorder the terms: 2x2 + 4y + 2y2 + -2z + 2z2 = 100 Solving 2x2 + 4y + 2y2 + -2z + 2z2 = 100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 2x2 + 4y + 2y2 + -2z + -4y + 2z2 = 100 + -4y Reorder the terms: 2x2 + 4y + -4y + 2y2 + -2z + 2z2 = 100 + -4y Combine like terms: 4y + -4y = 0 2x2 + 0 + 2y2 + -2z + 2z2 = 100 + -4y 2x2 + 2y2 + -2z + 2z2 = 100 + -4y Add '-2y2' to each side of the equation. 2x2 + 2y2 + -2z + -2y2 + 2z2 = 100 + -4y + -2y2 Reorder the terms: 2x2 + 2y2 + -2y2 + -2z + 2z2 = 100 + -4y + -2y2 Combine like terms: 2y2 + -2y2 = 0 2x2 + 0 + -2z + 2z2 = 100 + -4y + -2y2 2x2 + -2z + 2z2 = 100 + -4y + -2y2 Add '2z' to each side of the equation. 2x2 + -2z + 2z + 2z2 = 100 + -4y + -2y2 + 2z Combine like terms: -2z + 2z = 0 2x2 + 0 + 2z2 = 100 + -4y + -2y2 + 2z 2x2 + 2z2 = 100 + -4y + -2y2 + 2z Add '-2z2' to each side of the equation. 2x2 + 2z2 + -2z2 = 100 + -4y + -2y2 + 2z + -2z2 Combine like terms: 2z2 + -2z2 = 0 2x2 + 0 = 100 + -4y + -2y2 + 2z + -2z2 2x2 = 100 + -4y + -2y2 + 2z + -2z2 Divide each side by '2'. x2 = 50 + -2y + -1y2 + z + -1z2 Simplifying x2 = 50 + -2y + -1y2 + z + -1z2 Reorder the terms: -50 + x2 + 2y + y2 + -1z + z2 = 50 + -2y + -1y2 + z + -1z2 + -50 + 2y + y2 + -1z + z2 Reorder the terms: -50 + x2 + 2y + y2 + -1z + z2 = 50 + -50 + -2y + 2y + -1y2 + y2 + z + -1z + -1z2 + z2 Combine like terms: 50 + -50 = 0 -50 + x2 + 2y + y2 + -1z + z2 = 0 + -2y + 2y + -1y2 + y2 + z + -1z + -1z2 + z2 -50 + x2 + 2y + y2 + -1z + z2 = -2y + 2y + -1y2 + y2 + z + -1z + -1z2 + z2 Combine like terms: -2y + 2y = 0 -50 + x2 + 2y + y2 + -1z + z2 = 0 + -1y2 + y2 + z + -1z + -1z2 + z2 -50 + x2 + 2y + y2 + -1z + z2 = -1y2 + y2 + z + -1z + -1z2 + z2 Combine like terms: -1y2 + y2 = 0 -50 + x2 + 2y + y2 + -1z + z2 = 0 + z + -1z + -1z2 + z2 -50 + x2 + 2y + y2 + -1z + z2 = z + -1z + -1z2 + z2 Combine like terms: z + -1z = 0 -50 + x2 + 2y + y2 + -1z + z2 = 0 + -1z2 + z2 -50 + x2 + 2y + y2 + -1z + z2 = -1z2 + z2 Combine like terms: -1z2 + z2 = 0 -50 + x2 + 2y + y2 + -1z + z2 = 0 The solution to this equation could not be determined.
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