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Simplifying 2z(5z + -3) = 10z(2) + -48 Reorder the terms: 2z(-3 + 5z) = 10z(2) + -48 (-3 * 2z + 5z * 2z) = 10z(2) + -48 (-6z + 10z2) = 10z(2) + -48 Reorder the terms for easier multiplication: -6z + 10z2 = 10 * 2z + -48 Multiply 10 * 2 -6z + 10z2 = 20z + -48 Reorder the terms: -6z + 10z2 = -48 + 20z Solving -6z + 10z2 = -48 + 20z Solving for variable 'z'. Reorder the terms: 48 + -6z + -20z + 10z2 = -48 + 20z + 48 + -20z Combine like terms: -6z + -20z = -26z 48 + -26z + 10z2 = -48 + 20z + 48 + -20z Reorder the terms: 48 + -26z + 10z2 = -48 + 48 + 20z + -20z Combine like terms: -48 + 48 = 0 48 + -26z + 10z2 = 0 + 20z + -20z 48 + -26z + 10z2 = 20z + -20z Combine like terms: 20z + -20z = 0 48 + -26z + 10z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -13z + 5z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -13z + 5z2)' equal to zero and attempt to solve: Simplifying 24 + -13z + 5z2 = 0 Solving 24 + -13z + 5z2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.8 + -2.6z + z2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + -2.6z + -4.8 + z2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + -2.6z + z2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + -2.6z + z2 = 0 + -4.8 -2.6z + z2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 -2.6z + z2 = -4.8 The z term is -2.6z. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6z + 1.69 + z2 = -4.8 + 1.69 Reorder the terms: 1.69 + -2.6z + z2 = -4.8 + 1.69 Combine like terms: -4.8 + 1.69 = -3.11 1.69 + -2.6z + z2 = -3.11 Factor a perfect square on the left side: (z + -1.3)(z + -1.3) = -3.11 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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