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Simplifying -1[5z(11z + 7)] = 7 + (5z + 1) Reorder the terms: -1[5z(7 + 11z)] = 7 + (5z + 1) -1[(7 * 5z + 11z * 5z)] = 7 + (5z + 1) -1[(35z + 55z2)] = 7 + (5z + 1) [35z * -1 + 55z2 * -1] = 7 + (5z + 1) [-35z + -55z2] = 7 + (5z + 1) Reorder the terms: -35z + -55z2 = 7 + (1 + 5z) Remove parenthesis around (1 + 5z) -35z + -55z2 = 7 + 1 + 5z Combine like terms: 7 + 1 = 8 -35z + -55z2 = 8 + 5z Solving -35z + -55z2 = 8 + 5z Solving for variable 'z'. Reorder the terms: -8 + -35z + -5z + -55z2 = 8 + 5z + -8 + -5z Combine like terms: -35z + -5z = -40z -8 + -40z + -55z2 = 8 + 5z + -8 + -5z Reorder the terms: -8 + -40z + -55z2 = 8 + -8 + 5z + -5z Combine like terms: 8 + -8 = 0 -8 + -40z + -55z2 = 0 + 5z + -5z -8 + -40z + -55z2 = 5z + -5z Combine like terms: 5z + -5z = 0 -8 + -40z + -55z2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 40z + 55z2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 40z + 55z2)' equal to zero and attempt to solve: Simplifying 8 + 40z + 55z2 = 0 Solving 8 + 40z + 55z2 = 0 Begin completing the square. Divide all terms by 55 the coefficient of the squared term: Divide each side by '55'. 0.1454545455 + 0.7272727273z + z2 = 0 Move the constant term to the right: Add '-0.1454545455' to each side of the equation. 0.1454545455 + 0.7272727273z + -0.1454545455 + z2 = 0 + -0.1454545455 Reorder the terms: 0.1454545455 + -0.1454545455 + 0.7272727273z + z2 = 0 + -0.1454545455 Combine like terms: 0.1454545455 + -0.1454545455 = 0.0000000000 0.0000000000 + 0.7272727273z + z2 = 0 + -0.1454545455 0.7272727273z + z2 = 0 + -0.1454545455 Combine like terms: 0 + -0.1454545455 = -0.1454545455 0.7272727273z + z2 = -0.1454545455 The z term is 0.7272727273z. Take half its coefficient (0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. 0.7272727273z + 0.1322314050 + z2 = -0.1454545455 + 0.1322314050 Reorder the terms: 0.1322314050 + 0.7272727273z + z2 = -0.1454545455 + 0.1322314050 Combine like terms: -0.1454545455 + 0.1322314050 = -0.0132231405 0.1322314050 + 0.7272727273z + z2 = -0.0132231405 Factor a perfect square on the left side: (z + 0.3636363637)(z + 0.3636363637) = -0.0132231405 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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