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Simplifying 7z2 + 60z + -2 = 0 Reorder the terms: -2 + 60z + 7z2 = 0 Solving -2 + 60z + 7z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 8.571428571z + z2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 8.571428571z + 0.2857142857 + z2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 8.571428571z + z2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 8.571428571z + z2 = 0 + 0.2857142857 8.571428571z + z2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 8.571428571z + z2 = 0.2857142857 The z term is 8.571428571z. Take half its coefficient (4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. 8.571428571z + 18.36734694 + z2 = 0.2857142857 + 18.36734694 Reorder the terms: 18.36734694 + 8.571428571z + z2 = 0.2857142857 + 18.36734694 Combine like terms: 0.2857142857 + 18.36734694 = 18.6530612257 18.36734694 + 8.571428571z + z2 = 18.6530612257 Factor a perfect square on the left side: (z + 4.285714286)(z + 4.285714286) = 18.6530612257 Calculate the square root of the right side: 4.318918988 Break this problem into two subproblems by setting (z + 4.285714286) equal to 4.318918988 and -4.318918988.Subproblem 1
z + 4.285714286 = 4.318918988 Simplifying z + 4.285714286 = 4.318918988 Reorder the terms: 4.285714286 + z = 4.318918988 Solving 4.285714286 + z = 4.318918988 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + z = 4.318918988 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + z = 4.318918988 + -4.285714286 z = 4.318918988 + -4.285714286 Combine like terms: 4.318918988 + -4.285714286 = 0.033204702 z = 0.033204702 Simplifying z = 0.033204702Subproblem 2
z + 4.285714286 = -4.318918988 Simplifying z + 4.285714286 = -4.318918988 Reorder the terms: 4.285714286 + z = -4.318918988 Solving 4.285714286 + z = -4.318918988 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + z = -4.318918988 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + z = -4.318918988 + -4.285714286 z = -4.318918988 + -4.285714286 Combine like terms: -4.318918988 + -4.285714286 = -8.604633274 z = -8.604633274 Simplifying z = -8.604633274Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.033204702, -8.604633274}
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