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Simplifying z(z + 4) = 70 Reorder the terms: z(4 + z) = 70 (4 * z + z * z) = 70 (4z + z2) = 70 Solving 4z + z2 = 70 Solving for variable 'z'. Reorder the terms: -70 + 4z + z2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + 4z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + 4z + 70 + z2 = 0 + 70 Reorder the terms: -70 + 70 + 4z + z2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 4z + z2 = 0 + 70 4z + z2 = 0 + 70 Combine like terms: 0 + 70 = 70 4z + z2 = 70 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 = 70 + 4 Reorder the terms: 4 + 4z + z2 = 70 + 4 Combine like terms: 70 + 4 = 74 4 + 4z + z2 = 74 Factor a perfect square on the left side: (z + 2)(z + 2) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (z + 2) equal to 8.602325267 and -8.602325267.Subproblem 1
z + 2 = 8.602325267 Simplifying z + 2 = 8.602325267 Reorder the terms: 2 + z = 8.602325267 Solving 2 + z = 8.602325267 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 = 8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + z = 8.602325267 + -2 z = 8.602325267 + -2 Combine like terms: 8.602325267 + -2 = 6.602325267 z = 6.602325267 Simplifying z = 6.602325267Subproblem 2
z + 2 = -8.602325267 Simplifying z + 2 = -8.602325267 Reorder the terms: 2 + z = -8.602325267 Solving 2 + z = -8.602325267 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 = -8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + z = -8.602325267 + -2 z = -8.602325267 + -2 Combine like terms: -8.602325267 + -2 = -10.602325267 z = -10.602325267 Simplifying z = -10.602325267Solution
The solution to the problem is based on the solutions from the subproblems. z = {6.602325267, -10.602325267}
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