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Simplifying 0 = z2 + 4z + -20 Reorder the terms: 0 = -20 + 4z + z2 Solving 0 = -20 + 4z + z2 Solving for variable 'z'. Combine like terms: 0 + 20 = 20 20 + -4z + -1z2 = -20 + 4z + z2 + 20 + -4z + -1z2 Reorder the terms: 20 + -4z + -1z2 = -20 + 20 + 4z + -4z + z2 + -1z2 Combine like terms: -20 + 20 = 0 20 + -4z + -1z2 = 0 + 4z + -4z + z2 + -1z2 20 + -4z + -1z2 = 4z + -4z + z2 + -1z2 Combine like terms: 4z + -4z = 0 20 + -4z + -1z2 = 0 + z2 + -1z2 20 + -4z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 20 + -4z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + 4z + z2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 4z + 20 + z2 = 0 + 20 Reorder the terms: -20 + 20 + 4z + z2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 4z + z2 = 0 + 20 4z + z2 = 0 + 20 Combine like terms: 0 + 20 = 20 4z + z2 = 20 The z term is 4z. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4z + 4 + z2 = 20 + 4 Reorder the terms: 4 + 4z + z2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + 4z + z2 = 24 Factor a perfect square on the left side: (z + 2)(z + 2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (z + 2) equal to 4.898979486 and -4.898979486.Subproblem 1
z + 2 = 4.898979486 Simplifying z + 2 = 4.898979486 Reorder the terms: 2 + z = 4.898979486 Solving 2 + z = 4.898979486 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + z = 4.898979486 + -2 z = 4.898979486 + -2 Combine like terms: 4.898979486 + -2 = 2.898979486 z = 2.898979486 Simplifying z = 2.898979486Subproblem 2
z + 2 = -4.898979486 Simplifying z + 2 = -4.898979486 Reorder the terms: 2 + z = -4.898979486 Solving 2 + z = -4.898979486 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = -4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + z = -4.898979486 + -2 z = -4.898979486 + -2 Combine like terms: -4.898979486 + -2 = -6.898979486 z = -6.898979486 Simplifying z = -6.898979486Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.898979486, -6.898979486}
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