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Simplifying 5z2 + -9z + -7 = 0 Reorder the terms: -7 + -9z + 5z2 = 0 Solving -7 + -9z + 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 + -1.8z + z2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1.8z + 1.4 + z2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1.8z + z2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1.8z + z2 = 0 + 1.4 -1.8z + z2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1.8z + z2 = 1.4 The z term is -1.8z. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8z + 0.81 + z2 = 1.4 + 0.81 Reorder the terms: 0.81 + -1.8z + z2 = 1.4 + 0.81 Combine like terms: 1.4 + 0.81 = 2.21 0.81 + -1.8z + z2 = 2.21 Factor a perfect square on the left side: (z + -0.9)(z + -0.9) = 2.21 Calculate the square root of the right side: 1.486606875 Break this problem into two subproblems by setting (z + -0.9) equal to 1.486606875 and -1.486606875.Subproblem 1
z + -0.9 = 1.486606875 Simplifying z + -0.9 = 1.486606875 Reorder the terms: -0.9 + z = 1.486606875 Solving -0.9 + z = 1.486606875 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + z = 1.486606875 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + z = 1.486606875 + 0.9 z = 1.486606875 + 0.9 Combine like terms: 1.486606875 + 0.9 = 2.386606875 z = 2.386606875 Simplifying z = 2.386606875Subproblem 2
z + -0.9 = -1.486606875 Simplifying z + -0.9 = -1.486606875 Reorder the terms: -0.9 + z = -1.486606875 Solving -0.9 + z = -1.486606875 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + z = -1.486606875 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + z = -1.486606875 + 0.9 z = -1.486606875 + 0.9 Combine like terms: -1.486606875 + 0.9 = -0.586606875 z = -0.586606875 Simplifying z = -0.586606875Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.386606875, -0.586606875}
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