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Simplifying 25z2 + 60z + -39 = 0 Reorder the terms: -39 + 60z + 25z2 = 0 Solving -39 + 60z + 25z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.56 + 2.4z + z2 = 0 Move the constant term to the right: Add '1.56' to each side of the equation. -1.56 + 2.4z + 1.56 + z2 = 0 + 1.56 Reorder the terms: -1.56 + 1.56 + 2.4z + z2 = 0 + 1.56 Combine like terms: -1.56 + 1.56 = 0.00 0.00 + 2.4z + z2 = 0 + 1.56 2.4z + z2 = 0 + 1.56 Combine like terms: 0 + 1.56 = 1.56 2.4z + z2 = 1.56 The z term is 2.4z. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4z + 1.44 + z2 = 1.56 + 1.44 Reorder the terms: 1.44 + 2.4z + z2 = 1.56 + 1.44 Combine like terms: 1.56 + 1.44 = 3 1.44 + 2.4z + z2 = 3 Factor a perfect square on the left side: (z + 1.2)(z + 1.2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (z + 1.2) equal to 1.732050808 and -1.732050808.Subproblem 1
z + 1.2 = 1.732050808 Simplifying z + 1.2 = 1.732050808 Reorder the terms: 1.2 + z = 1.732050808 Solving 1.2 + z = 1.732050808 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + z = 1.732050808 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + z = 1.732050808 + -1.2 z = 1.732050808 + -1.2 Combine like terms: 1.732050808 + -1.2 = 0.532050808 z = 0.532050808 Simplifying z = 0.532050808Subproblem 2
z + 1.2 = -1.732050808 Simplifying z + 1.2 = -1.732050808 Reorder the terms: 1.2 + z = -1.732050808 Solving 1.2 + z = -1.732050808 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + z = -1.732050808 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + z = -1.732050808 + -1.2 z = -1.732050808 + -1.2 Combine like terms: -1.732050808 + -1.2 = -2.932050808 z = -2.932050808 Simplifying z = -2.932050808Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.532050808, -2.932050808}
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