7(z-3)8z-2=

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Solution for 7(z-3)8z-2= equation:


Simplifying
7(z + -3) * 8z + -2 = 0

Reorder the terms:
7(-3 + z) * 8z + -2 = 0

Reorder the terms for easier multiplication:
7 * 8z(-3 + z) + -2 = 0

Multiply 7 * 8
56z(-3 + z) + -2 = 0
(-3 * 56z + z * 56z) + -2 = 0
(-168z + 56z2) + -2 = 0

Reorder the terms:
-2 + -168z + 56z2 = 0

Solving
-2 + -168z + 56z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -84z + 28z2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -84z + 28z2)' equal to zero and attempt to solve: Simplifying -1 + -84z + 28z2 = 0 Solving -1 + -84z + 28z2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.03571428571 + -3z + z2 = 0 Move the constant term to the right: Add '0.03571428571' to each side of the equation. -0.03571428571 + -3z + 0.03571428571 + z2 = 0 + 0.03571428571 Reorder the terms: -0.03571428571 + 0.03571428571 + -3z + z2 = 0 + 0.03571428571 Combine like terms: -0.03571428571 + 0.03571428571 = 0.00000000000 0.00000000000 + -3z + z2 = 0 + 0.03571428571 -3z + z2 = 0 + 0.03571428571 Combine like terms: 0 + 0.03571428571 = 0.03571428571 -3z + z2 = 0.03571428571 The z term is -3z. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3z + 2.25 + z2 = 0.03571428571 + 2.25 Reorder the terms: 2.25 + -3z + z2 = 0.03571428571 + 2.25 Combine like terms: 0.03571428571 + 2.25 = 2.28571428571 2.25 + -3z + z2 = 2.28571428571 Factor a perfect square on the left side: (z + -1.5)(z + -1.5) = 2.28571428571 Calculate the square root of the right side: 1.511857892 Break this problem into two subproblems by setting (z + -1.5) equal to 1.511857892 and -1.511857892.

Subproblem 1

z + -1.5 = 1.511857892 Simplifying z + -1.5 = 1.511857892 Reorder the terms: -1.5 + z = 1.511857892 Solving -1.5 + z = 1.511857892 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + z = 1.511857892 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + z = 1.511857892 + 1.5 z = 1.511857892 + 1.5 Combine like terms: 1.511857892 + 1.5 = 3.011857892 z = 3.011857892 Simplifying z = 3.011857892

Subproblem 2

z + -1.5 = -1.511857892 Simplifying z + -1.5 = -1.511857892 Reorder the terms: -1.5 + z = -1.511857892 Solving -1.5 + z = -1.511857892 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + z = -1.511857892 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + z = -1.511857892 + 1.5 z = -1.511857892 + 1.5 Combine like terms: -1.511857892 + 1.5 = -0.011857892 z = -0.011857892 Simplifying z = -0.011857892

Solution

The solution to the problem is based on the solutions from the subproblems. z = {3.011857892, -0.011857892}

Solution

z = {3.011857892, -0.011857892}

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