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Simplifying -1[10z(19z + 3)] = 3 + (8z + 10) Reorder the terms: -1[10z(3 + 19z)] = 3 + (8z + 10) -1[(3 * 10z + 19z * 10z)] = 3 + (8z + 10) -1[(30z + 190z2)] = 3 + (8z + 10) [30z * -1 + 190z2 * -1] = 3 + (8z + 10) [-30z + -190z2] = 3 + (8z + 10) Reorder the terms: -30z + -190z2 = 3 + (10 + 8z) Remove parenthesis around (10 + 8z) -30z + -190z2 = 3 + 10 + 8z Combine like terms: 3 + 10 = 13 -30z + -190z2 = 13 + 8z Solving -30z + -190z2 = 13 + 8z Solving for variable 'z'. Reorder the terms: -13 + -30z + -8z + -190z2 = 13 + 8z + -13 + -8z Combine like terms: -30z + -8z = -38z -13 + -38z + -190z2 = 13 + 8z + -13 + -8z Reorder the terms: -13 + -38z + -190z2 = 13 + -13 + 8z + -8z Combine like terms: 13 + -13 = 0 -13 + -38z + -190z2 = 0 + 8z + -8z -13 + -38z + -190z2 = 8z + -8z Combine like terms: 8z + -8z = 0 -13 + -38z + -190z2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 38z + 190z2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 38z + 190z2)' equal to zero and attempt to solve: Simplifying 13 + 38z + 190z2 = 0 Solving 13 + 38z + 190z2 = 0 Begin completing the square. Divide all terms by 190 the coefficient of the squared term: Divide each side by '190'. 0.06842105263 + 0.2z + z2 = 0.0 Move the constant term to the right: Add '-0.06842105263' to each side of the equation. 0.06842105263 + 0.2z + -0.06842105263 + z2 = 0.0 + -0.06842105263 Reorder the terms: 0.06842105263 + -0.06842105263 + 0.2z + z2 = 0.0 + -0.06842105263 Combine like terms: 0.06842105263 + -0.06842105263 = 0.00000000000 0.00000000000 + 0.2z + z2 = 0.0 + -0.06842105263 0.2z + z2 = 0.0 + -0.06842105263 Combine like terms: 0.0 + -0.06842105263 = -0.06842105263 0.2z + z2 = -0.06842105263 The z term is 0.2z. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2z + 0.01 + z2 = -0.06842105263 + 0.01 Reorder the terms: 0.01 + 0.2z + z2 = -0.06842105263 + 0.01 Combine like terms: -0.06842105263 + 0.01 = -0.05842105263 0.01 + 0.2z + z2 = -0.05842105263 Factor a perfect square on the left side: (z + 0.1)(z + 0.1) = -0.05842105263 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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