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Simplifying -1[10z(20z + 7)] = 7 + (9z + 8) Reorder the terms: -1[10z(7 + 20z)] = 7 + (9z + 8) -1[(7 * 10z + 20z * 10z)] = 7 + (9z + 8) -1[(70z + 200z2)] = 7 + (9z + 8) [70z * -1 + 200z2 * -1] = 7 + (9z + 8) [-70z + -200z2] = 7 + (9z + 8) Reorder the terms: -70z + -200z2 = 7 + (8 + 9z) Remove parenthesis around (8 + 9z) -70z + -200z2 = 7 + 8 + 9z Combine like terms: 7 + 8 = 15 -70z + -200z2 = 15 + 9z Solving -70z + -200z2 = 15 + 9z Solving for variable 'z'. Reorder the terms: -15 + -70z + -9z + -200z2 = 15 + 9z + -15 + -9z Combine like terms: -70z + -9z = -79z -15 + -79z + -200z2 = 15 + 9z + -15 + -9z Reorder the terms: -15 + -79z + -200z2 = 15 + -15 + 9z + -9z Combine like terms: 15 + -15 = 0 -15 + -79z + -200z2 = 0 + 9z + -9z -15 + -79z + -200z2 = 9z + -9z Combine like terms: 9z + -9z = 0 -15 + -79z + -200z2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 79z + 200z2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 79z + 200z2)' equal to zero and attempt to solve: Simplifying 15 + 79z + 200z2 = 0 Solving 15 + 79z + 200z2 = 0 Begin completing the square. Divide all terms by 200 the coefficient of the squared term: Divide each side by '200'. 0.075 + 0.395z + z2 = 0.00 Move the constant term to the right: Add '-0.075' to each side of the equation. 0.075 + 0.395z + -0.075 + z2 = 0.00 + -0.075 Reorder the terms: 0.075 + -0.075 + 0.395z + z2 = 0.00 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + 0.395z + z2 = 0.00 + -0.075 0.395z + z2 = 0.00 + -0.075 Combine like terms: 0.00 + -0.075 = -0.075 0.395z + z2 = -0.075 The z term is 0.395z. Take half its coefficient (0.1975). Square it (0.03900625) and add it to both sides. Add '0.03900625' to each side of the equation. 0.395z + 0.03900625 + z2 = -0.075 + 0.03900625 Reorder the terms: 0.03900625 + 0.395z + z2 = -0.075 + 0.03900625 Combine like terms: -0.075 + 0.03900625 = -0.03599375 0.03900625 + 0.395z + z2 = -0.03599375 Factor a perfect square on the left side: (z + 0.1975)(z + 0.1975) = -0.03599375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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