24q^2-90q=21

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Solution for 24q^2-90q=21 equation:


Simplifying
24q2 + -90q = 21

Reorder the terms:
-90q + 24q2 = 21

Solving
-90q + 24q2 = 21

Solving for variable 'q'.

Reorder the terms:
-21 + -90q + 24q2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -90q + 24q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -30q + 8q2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-7 + -30q + 8q2)' equal to zero and attempt to solve: Simplifying -7 + -30q + 8q2 = 0 Solving -7 + -30q + 8q2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -3.75q + q2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -3.75q + 0.875 + q2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -3.75q + q2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -3.75q + q2 = 0 + 0.875 -3.75q + q2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -3.75q + q2 = 0.875 The q term is -3.75q. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75q + 3.515625 + q2 = 0.875 + 3.515625 Reorder the terms: 3.515625 + -3.75q + q2 = 0.875 + 3.515625 Combine like terms: 0.875 + 3.515625 = 4.390625 3.515625 + -3.75q + q2 = 4.390625 Factor a perfect square on the left side: (q + -1.875)(q + -1.875) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (q + -1.875) equal to 2.095381827 and -2.095381827.

Subproblem 1

q + -1.875 = 2.095381827 Simplifying q + -1.875 = 2.095381827 Reorder the terms: -1.875 + q = 2.095381827 Solving -1.875 + q = 2.095381827 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + q = 2.095381827 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + q = 2.095381827 + 1.875 q = 2.095381827 + 1.875 Combine like terms: 2.095381827 + 1.875 = 3.970381827 q = 3.970381827 Simplifying q = 3.970381827

Subproblem 2

q + -1.875 = -2.095381827 Simplifying q + -1.875 = -2.095381827 Reorder the terms: -1.875 + q = -2.095381827 Solving -1.875 + q = -2.095381827 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + q = -2.095381827 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + q = -2.095381827 + 1.875 q = -2.095381827 + 1.875 Combine like terms: -2.095381827 + 1.875 = -0.220381827 q = -0.220381827 Simplifying q = -0.220381827

Solution

The solution to the problem is based on the solutions from the subproblems. q = {3.970381827, -0.220381827}

Solution

q = {3.970381827, -0.220381827}

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