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Simplifying 5z2 + 70z + -20 = 0 Reorder the terms: -20 + 70z + 5z2 = 0 Solving -20 + 70z + 5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + 14z + z2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + 14z + z2)' equal to zero and attempt to solve: Simplifying -4 + 14z + z2 = 0 Solving -4 + 14z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 14z + 4 + z2 = 0 + 4 Reorder the terms: -4 + 4 + 14z + z2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 14z + z2 = 0 + 4 14z + z2 = 0 + 4 Combine like terms: 0 + 4 = 4 14z + z2 = 4 The z term is 14z. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14z + 49 + z2 = 4 + 49 Reorder the terms: 49 + 14z + z2 = 4 + 49 Combine like terms: 4 + 49 = 53 49 + 14z + z2 = 53 Factor a perfect square on the left side: (z + 7)(z + 7) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (z + 7) equal to 7.280109889 and -7.280109889.Subproblem 1
z + 7 = 7.280109889 Simplifying z + 7 = 7.280109889 Reorder the terms: 7 + z = 7.280109889 Solving 7 + z = 7.280109889 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = 7.280109889 + -7 Combine like terms: 7 + -7 = 0 0 + z = 7.280109889 + -7 z = 7.280109889 + -7 Combine like terms: 7.280109889 + -7 = 0.280109889 z = 0.280109889 Simplifying z = 0.280109889Subproblem 2
z + 7 = -7.280109889 Simplifying z + 7 = -7.280109889 Reorder the terms: 7 + z = -7.280109889 Solving 7 + z = -7.280109889 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = -7.280109889 + -7 Combine like terms: 7 + -7 = 0 0 + z = -7.280109889 + -7 z = -7.280109889 + -7 Combine like terms: -7.280109889 + -7 = -14.280109889 z = -14.280109889 Simplifying z = -14.280109889Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.280109889, -14.280109889}Solution
z = {0.280109889, -14.280109889}
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