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Simplifying 3z2 + -15z + -21 = 0 Reorder the terms: -21 + -15z + 3z2 = 0 Solving -21 + -15z + 3z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -5z + z2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -5z + z2)' equal to zero and attempt to solve: Simplifying -7 + -5z + z2 = 0 Solving -7 + -5z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -5z + 7 + z2 = 0 + 7 Reorder the terms: -7 + 7 + -5z + z2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5z + z2 = 0 + 7 -5z + z2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5z + z2 = 7 The z term is -5z. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5z + 6.25 + z2 = 7 + 6.25 Reorder the terms: 6.25 + -5z + z2 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + -5z + z2 = 13.25 Factor a perfect square on the left side: (z + -2.5)(z + -2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (z + -2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
z + -2.5 = 3.640054945 Simplifying z + -2.5 = 3.640054945 Reorder the terms: -2.5 + z = 3.640054945 Solving -2.5 + z = 3.640054945 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = 3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = 3.640054945 + 2.5 z = 3.640054945 + 2.5 Combine like terms: 3.640054945 + 2.5 = 6.140054945 z = 6.140054945 Simplifying z = 6.140054945Subproblem 2
z + -2.5 = -3.640054945 Simplifying z + -2.5 = -3.640054945 Reorder the terms: -2.5 + z = -3.640054945 Solving -2.5 + z = -3.640054945 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = -3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = -3.640054945 + 2.5 z = -3.640054945 + 2.5 Combine like terms: -3.640054945 + 2.5 = -1.140054945 z = -1.140054945 Simplifying z = -1.140054945Solution
The solution to the problem is based on the solutions from the subproblems. z = {6.140054945, -1.140054945}Solution
z = {6.140054945, -1.140054945}
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