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Simplifying y2 + -4z2 + 4x + -6y + -24z + -31 = 0 Reorder the terms: -31 + 4x + -6y + y2 + -24z + -4z2 = 0 Solving -31 + 4x + -6y + y2 + -24z + -4z2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 4x + -6y + y2 + -24z + 31 + -4z2 = 0 + 31 Reorder the terms: -31 + 31 + 4x + -6y + y2 + -24z + -4z2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 4x + -6y + y2 + -24z + -4z2 = 0 + 31 4x + -6y + y2 + -24z + -4z2 = 0 + 31 Combine like terms: 0 + 31 = 31 4x + -6y + y2 + -24z + -4z2 = 31 Add '6y' to each side of the equation. 4x + -6y + y2 + -24z + 6y + -4z2 = 31 + 6y Reorder the terms: 4x + -6y + 6y + y2 + -24z + -4z2 = 31 + 6y Combine like terms: -6y + 6y = 0 4x + 0 + y2 + -24z + -4z2 = 31 + 6y 4x + y2 + -24z + -4z2 = 31 + 6y Add '-1y2' to each side of the equation. 4x + y2 + -24z + -1y2 + -4z2 = 31 + 6y + -1y2 Reorder the terms: 4x + y2 + -1y2 + -24z + -4z2 = 31 + 6y + -1y2 Combine like terms: y2 + -1y2 = 0 4x + 0 + -24z + -4z2 = 31 + 6y + -1y2 4x + -24z + -4z2 = 31 + 6y + -1y2 Add '24z' to each side of the equation. 4x + -24z + 24z + -4z2 = 31 + 6y + -1y2 + 24z Combine like terms: -24z + 24z = 0 4x + 0 + -4z2 = 31 + 6y + -1y2 + 24z 4x + -4z2 = 31 + 6y + -1y2 + 24z Add '4z2' to each side of the equation. 4x + -4z2 + 4z2 = 31 + 6y + -1y2 + 24z + 4z2 Combine like terms: -4z2 + 4z2 = 0 4x + 0 = 31 + 6y + -1y2 + 24z + 4z2 4x = 31 + 6y + -1y2 + 24z + 4z2 Divide each side by '4'. x = 7.75 + 1.5y + -0.25y2 + 6z + z2 Simplifying x = 7.75 + 1.5y + -0.25y2 + 6z + z2
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