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Simplifying z2 + -24z = -49 Reorder the terms: -24z + z2 = -49 Solving -24z + z2 = -49 Solving for variable 'z'. Reorder the terms: 49 + -24z + z2 = -49 + 49 Combine like terms: -49 + 49 = 0 49 + -24z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -24z + -49 + z2 = 0 + -49 Reorder the terms: 49 + -49 + -24z + z2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -24z + z2 = 0 + -49 -24z + z2 = 0 + -49 Combine like terms: 0 + -49 = -49 -24z + z2 = -49 The z term is -24z. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24z + 144 + z2 = -49 + 144 Reorder the terms: 144 + -24z + z2 = -49 + 144 Combine like terms: -49 + 144 = 95 144 + -24z + z2 = 95 Factor a perfect square on the left side: (z + -12)(z + -12) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (z + -12) equal to 9.746794345 and -9.746794345.Subproblem 1
z + -12 = 9.746794345 Simplifying z + -12 = 9.746794345 Reorder the terms: -12 + z = 9.746794345 Solving -12 + z = 9.746794345 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + z = 9.746794345 + 12 Combine like terms: -12 + 12 = 0 0 + z = 9.746794345 + 12 z = 9.746794345 + 12 Combine like terms: 9.746794345 + 12 = 21.746794345 z = 21.746794345 Simplifying z = 21.746794345Subproblem 2
z + -12 = -9.746794345 Simplifying z + -12 = -9.746794345 Reorder the terms: -12 + z = -9.746794345 Solving -12 + z = -9.746794345 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + z = -9.746794345 + 12 Combine like terms: -12 + 12 = 0 0 + z = -9.746794345 + 12 z = -9.746794345 + 12 Combine like terms: -9.746794345 + 12 = 2.253205655 z = 2.253205655 Simplifying z = 2.253205655Solution
The solution to the problem is based on the solutions from the subproblems. z = {21.746794345, 2.253205655}
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