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Simplifying (4z + -7)(4z + -7) + -1(z + 5)(z + 5) = 0 Reorder the terms: (-7 + 4z)(4z + -7) + -1(z + 5)(z + 5) = 0 Reorder the terms: (-7 + 4z)(-7 + 4z) + -1(z + 5)(z + 5) = 0 Multiply (-7 + 4z) * (-7 + 4z) (-7(-7 + 4z) + 4z * (-7 + 4z)) + -1(z + 5)(z + 5) = 0 ((-7 * -7 + 4z * -7) + 4z * (-7 + 4z)) + -1(z + 5)(z + 5) = 0 ((49 + -28z) + 4z * (-7 + 4z)) + -1(z + 5)(z + 5) = 0 (49 + -28z + (-7 * 4z + 4z * 4z)) + -1(z + 5)(z + 5) = 0 (49 + -28z + (-28z + 16z2)) + -1(z + 5)(z + 5) = 0 Combine like terms: -28z + -28z = -56z (49 + -56z + 16z2) + -1(z + 5)(z + 5) = 0 Reorder the terms: 49 + -56z + 16z2 + -1(5 + z)(z + 5) = 0 Reorder the terms: 49 + -56z + 16z2 + -1(5 + z)(5 + z) = 0 Multiply (5 + z) * (5 + z) 49 + -56z + 16z2 + -1(5(5 + z) + z(5 + z)) = 0 49 + -56z + 16z2 + -1((5 * 5 + z * 5) + z(5 + z)) = 0 49 + -56z + 16z2 + -1((25 + 5z) + z(5 + z)) = 0 49 + -56z + 16z2 + -1(25 + 5z + (5 * z + z * z)) = 0 49 + -56z + 16z2 + -1(25 + 5z + (5z + z2)) = 0 Combine like terms: 5z + 5z = 10z 49 + -56z + 16z2 + -1(25 + 10z + z2) = 0 49 + -56z + 16z2 + (25 * -1 + 10z * -1 + z2 * -1) = 0 49 + -56z + 16z2 + (-25 + -10z + -1z2) = 0 Reorder the terms: 49 + -25 + -56z + -10z + 16z2 + -1z2 = 0 Combine like terms: 49 + -25 = 24 24 + -56z + -10z + 16z2 + -1z2 = 0 Combine like terms: -56z + -10z = -66z 24 + -66z + 16z2 + -1z2 = 0 Combine like terms: 16z2 + -1z2 = 15z2 24 + -66z + 15z2 = 0 Solving 24 + -66z + 15z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -22z + 5z2) = 0 Factor a trinomial. 3((2 + -5z)(4 + -1z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -5z)' equal to zero and attempt to solve: Simplifying 2 + -5z = 0 Solving 2 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5z = 0 + -2 -5z = 0 + -2 Combine like terms: 0 + -2 = -2 -5z = -2 Divide each side by '-5'. z = 0.4 Simplifying z = 0.4Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Solution
z = {0.4, 4}
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