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Simplifying 5z2 + -2z + -2 = 0 Reorder the terms: -2 + -2z + 5z2 = 0 Solving -2 + -2z + 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'. -0.4 + -0.4z + z2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.4z + 0.4 + z2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.4z + z2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.4z + z2 = 0 + 0.4 -0.4z + z2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.4z + z2 = 0.4 The z term is -0.4z. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4z + 0.04 + z2 = 0.4 + 0.04 Reorder the terms: 0.04 + -0.4z + z2 = 0.4 + 0.04 Combine like terms: 0.4 + 0.04 = 0.44 0.04 + -0.4z + z2 = 0.44 Factor a perfect square on the left side: (z + -0.2)(z + -0.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (z + -0.2) equal to 0.663324958 and -0.663324958.Subproblem 1
z + -0.2 = 0.663324958 Simplifying z + -0.2 = 0.663324958 Reorder the terms: -0.2 + z = 0.663324958 Solving -0.2 + z = 0.663324958 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + z = 0.663324958 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + z = 0.663324958 + 0.2 z = 0.663324958 + 0.2 Combine like terms: 0.663324958 + 0.2 = 0.863324958 z = 0.863324958 Simplifying z = 0.863324958Subproblem 2
z + -0.2 = -0.663324958 Simplifying z + -0.2 = -0.663324958 Reorder the terms: -0.2 + z = -0.663324958 Solving -0.2 + z = -0.663324958 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + z = -0.663324958 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + z = -0.663324958 + 0.2 z = -0.663324958 + 0.2 Combine like terms: -0.663324958 + 0.2 = -0.463324958 z = -0.463324958 Simplifying z = -0.463324958Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.863324958, -0.463324958}
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