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Simplifying 15z2 + 7 = 20z + -3 Reorder the terms: 7 + 15z2 = 20z + -3 Reorder the terms: 7 + 15z2 = -3 + 20z Solving 7 + 15z2 = -3 + 20z Solving for variable 'z'. Reorder the terms: 7 + 3 + -20z + 15z2 = -3 + 20z + 3 + -20z Combine like terms: 7 + 3 = 10 10 + -20z + 15z2 = -3 + 20z + 3 + -20z Reorder the terms: 10 + -20z + 15z2 = -3 + 3 + 20z + -20z Combine like terms: -3 + 3 = 0 10 + -20z + 15z2 = 0 + 20z + -20z 10 + -20z + 15z2 = 20z + -20z Combine like terms: 20z + -20z = 0 10 + -20z + 15z2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -4z + 3z2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -4z + 3z2)' equal to zero and attempt to solve: Simplifying 2 + -4z + 3z2 = 0 Solving 2 + -4z + 3z2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -1.333333333z + z2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -1.333333333z + -0.6666666667 + z2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -1.333333333z + z2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -1.333333333z + z2 = 0 + -0.6666666667 -1.333333333z + z2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -1.333333333z + z2 = -0.6666666667 The z term is -1.333333333z. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333z + 0.4444444442 + z2 = -0.6666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333z + z2 = -0.6666666667 + 0.4444444442 Combine like terms: -0.6666666667 + 0.4444444442 = -0.2222222225 0.4444444442 + -1.333333333z + z2 = -0.2222222225 Factor a perfect square on the left side: (z + -0.6666666665)(z + -0.6666666665) = -0.2222222225 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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