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Simplifying 5z2 + 4z + -13 = 0 Reorder the terms: -13 + 4z + 5z2 = 0 Solving -13 + 4z + 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'. -2.6 + 0.8z + z2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 0.8z + 2.6 + z2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 0.8z + z2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 0.8z + z2 = 0 + 2.6 0.8z + z2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 0.8z + z2 = 2.6 The z term is 0.8z. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8z + 0.16 + z2 = 2.6 + 0.16 Reorder the terms: 0.16 + 0.8z + z2 = 2.6 + 0.16 Combine like terms: 2.6 + 0.16 = 2.76 0.16 + 0.8z + z2 = 2.76 Factor a perfect square on the left side: (z + 0.4)(z + 0.4) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (z + 0.4) equal to 1.661324773 and -1.661324773.Subproblem 1
z + 0.4 = 1.661324773 Simplifying z + 0.4 = 1.661324773 Reorder the terms: 0.4 + z = 1.661324773 Solving 0.4 + z = 1.661324773 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + z = 1.661324773 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + z = 1.661324773 + -0.4 z = 1.661324773 + -0.4 Combine like terms: 1.661324773 + -0.4 = 1.261324773 z = 1.261324773 Simplifying z = 1.261324773Subproblem 2
z + 0.4 = -1.661324773 Simplifying z + 0.4 = -1.661324773 Reorder the terms: 0.4 + z = -1.661324773 Solving 0.4 + z = -1.661324773 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + z = -1.661324773 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + z = -1.661324773 + -0.4 z = -1.661324773 + -0.4 Combine like terms: -1.661324773 + -0.4 = -2.061324773 z = -2.061324773 Simplifying z = -2.061324773Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.261324773, -2.061324773}
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