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Simplifying 5z2 + 36z + -7 = 0 Reorder the terms: -7 + 36z + 5z2 = 0 Solving -7 + 36z + 5z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 7.2z + z2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 7.2z + 1.4 + z2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 7.2z + z2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 7.2z + z2 = 0 + 1.4 7.2z + z2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 7.2z + z2 = 1.4 The z term is 7.2z. Take half its coefficient (3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. 7.2z + 12.96 + z2 = 1.4 + 12.96 Reorder the terms: 12.96 + 7.2z + z2 = 1.4 + 12.96 Combine like terms: 1.4 + 12.96 = 14.36 12.96 + 7.2z + z2 = 14.36 Factor a perfect square on the left side: (z + 3.6)(z + 3.6) = 14.36 Calculate the square root of the right side: 3.789459064 Break this problem into two subproblems by setting (z + 3.6) equal to 3.789459064 and -3.789459064.Subproblem 1
z + 3.6 = 3.789459064 Simplifying z + 3.6 = 3.789459064 Reorder the terms: 3.6 + z = 3.789459064 Solving 3.6 + z = 3.789459064 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + z = 3.789459064 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + z = 3.789459064 + -3.6 z = 3.789459064 + -3.6 Combine like terms: 3.789459064 + -3.6 = 0.189459064 z = 0.189459064 Simplifying z = 0.189459064Subproblem 2
z + 3.6 = -3.789459064 Simplifying z + 3.6 = -3.789459064 Reorder the terms: 3.6 + z = -3.789459064 Solving 3.6 + z = -3.789459064 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + z = -3.789459064 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + z = -3.789459064 + -3.6 z = -3.789459064 + -3.6 Combine like terms: -3.789459064 + -3.6 = -7.389459064 z = -7.389459064 Simplifying z = -7.389459064Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.189459064, -7.389459064}
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