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Simplifying (z2 + -3z + 4)(z2 + 3z + 4) = 0 Reorder the terms: (4 + -3z + z2)(z2 + 3z + 4) = 0 Reorder the terms: (4 + -3z + z2)(4 + 3z + z2) = 0 Multiply (4 + -3z + z2) * (4 + 3z + z2) (4(4 + 3z + z2) + -3z * (4 + 3z + z2) + z2(4 + 3z + z2)) = 0 ((4 * 4 + 3z * 4 + z2 * 4) + -3z * (4 + 3z + z2) + z2(4 + 3z + z2)) = 0 ((16 + 12z + 4z2) + -3z * (4 + 3z + z2) + z2(4 + 3z + z2)) = 0 (16 + 12z + 4z2 + (4 * -3z + 3z * -3z + z2 * -3z) + z2(4 + 3z + z2)) = 0 (16 + 12z + 4z2 + (-12z + -9z2 + -3z3) + z2(4 + 3z + z2)) = 0 (16 + 12z + 4z2 + -12z + -9z2 + -3z3 + (4 * z2 + 3z * z2 + z2 * z2)) = 0 (16 + 12z + 4z2 + -12z + -9z2 + -3z3 + (4z2 + 3z3 + z4)) = 0 Reorder the terms: (16 + 12z + -12z + 4z2 + -9z2 + 4z2 + -3z3 + 3z3 + z4) = 0 Combine like terms: 12z + -12z = 0 (16 + 0 + 4z2 + -9z2 + 4z2 + -3z3 + 3z3 + z4) = 0 (16 + 4z2 + -9z2 + 4z2 + -3z3 + 3z3 + z4) = 0 Combine like terms: 4z2 + -9z2 = -5z2 (16 + -5z2 + 4z2 + -3z3 + 3z3 + z4) = 0 Combine like terms: -5z2 + 4z2 = -1z2 (16 + -1z2 + -3z3 + 3z3 + z4) = 0 Combine like terms: -3z3 + 3z3 = 0 (16 + -1z2 + 0 + z4) = 0 (16 + -1z2 + z4) = 0 Solving 16 + -1z2 + z4 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -1z2 + -16 + z4 = 0 + -16 Reorder the terms: 16 + -16 + -1z2 + z4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1z2 + z4 = 0 + -16 -1z2 + z4 = 0 + -16 Combine like terms: 0 + -16 = -16 -1z2 + z4 = -16 The z term is -1z2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1z2 + 0.25 + z4 = -16 + 0.25 Reorder the terms: 0.25 + -1z2 + z4 = -16 + 0.25 Combine like terms: -16 + 0.25 = -15.75 0.25 + -1z2 + z4 = -15.75 Factor a perfect square on the left side: (z2 + -0.5)(z2 + -0.5) = -15.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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