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Simplifying -2z2 + -12z = -26 Reorder the terms: -12z + -2z2 = -26 Solving -12z + -2z2 = -26 Solving for variable 'z'. Reorder the terms: 26 + -12z + -2z2 = -26 + 26 Combine like terms: -26 + 26 = 0 26 + -12z + -2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -6z + -1z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -6z + -1z2)' equal to zero and attempt to solve: Simplifying 13 + -6z + -1z2 = 0 Solving 13 + -6z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + 6z + z2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 6z + 13 + z2 = 0 + 13 Reorder the terms: -13 + 13 + 6z + z2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 6z + z2 = 0 + 13 6z + z2 = 0 + 13 Combine like terms: 0 + 13 = 13 6z + z2 = 13 The z term is 6z. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6z + 9 + z2 = 13 + 9 Reorder the terms: 9 + 6z + z2 = 13 + 9 Combine like terms: 13 + 9 = 22 9 + 6z + z2 = 22 Factor a perfect square on the left side: (z + 3)(z + 3) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (z + 3) equal to 4.69041576 and -4.69041576.Subproblem 1
z + 3 = 4.69041576 Simplifying z + 3 = 4.69041576 Reorder the terms: 3 + z = 4.69041576 Solving 3 + z = 4.69041576 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = 4.69041576 + -3 Combine like terms: 3 + -3 = 0 0 + z = 4.69041576 + -3 z = 4.69041576 + -3 Combine like terms: 4.69041576 + -3 = 1.69041576 z = 1.69041576 Simplifying z = 1.69041576Subproblem 2
z + 3 = -4.69041576 Simplifying z + 3 = -4.69041576 Reorder the terms: 3 + z = -4.69041576 Solving 3 + z = -4.69041576 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = -4.69041576 + -3 Combine like terms: 3 + -3 = 0 0 + z = -4.69041576 + -3 z = -4.69041576 + -3 Combine like terms: -4.69041576 + -3 = -7.69041576 z = -7.69041576 Simplifying z = -7.69041576Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.69041576, -7.69041576}Solution
z = {1.69041576, -7.69041576}
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