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Simplifying 16(z + -1)(z + -1) + -29 = -28 Reorder the terms: 16(-1 + z)(z + -1) + -29 = -28 Reorder the terms: 16(-1 + z)(-1 + z) + -29 = -28 Multiply (-1 + z) * (-1 + z) 16(-1(-1 + z) + z(-1 + z)) + -29 = -28 16((-1 * -1 + z * -1) + z(-1 + z)) + -29 = -28 16((1 + -1z) + z(-1 + z)) + -29 = -28 16(1 + -1z + (-1 * z + z * z)) + -29 = -28 16(1 + -1z + (-1z + z2)) + -29 = -28 Combine like terms: -1z + -1z = -2z 16(1 + -2z + z2) + -29 = -28 (1 * 16 + -2z * 16 + z2 * 16) + -29 = -28 (16 + -32z + 16z2) + -29 = -28 Reorder the terms: 16 + -29 + -32z + 16z2 = -28 Combine like terms: 16 + -29 = -13 -13 + -32z + 16z2 = -28 Solving -13 + -32z + 16z2 = -28 Solving for variable 'z'. Reorder the terms: -13 + 28 + -32z + 16z2 = -28 + 28 Combine like terms: -13 + 28 = 15 15 + -32z + 16z2 = -28 + 28 Combine like terms: -28 + 28 = 0 15 + -32z + 16z2 = 0 Factor a trinomial. (3 + -4z)(5 + -4z) = 0Subproblem 1
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Subproblem 2
Set the factor '(5 + -4z)' equal to zero and attempt to solve: Simplifying 5 + -4z = 0 Solving 5 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4z = 0 + -5 -4z = 0 + -5 Combine like terms: 0 + -5 = -5 -4z = -5 Divide each side by '-4'. z = 1.25 Simplifying z = 1.25Solution
z = {0.75, 1.25}
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