8s(8+6s)=20

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Solution for 8s(8+6s)=20 equation:


Simplifying
8s(8 + 6s) = 20
(8 * 8s + 6s * 8s) = 20
(64s + 48s2) = 20

Solving
64s + 48s2 = 20

Solving for variable 's'.

Reorder the terms:
-20 + 64s + 48s2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 64s + 48s2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 16s + 12s2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-5 + 16s + 12s2)' equal to zero and attempt to solve: Simplifying -5 + 16s + 12s2 = 0 Solving -5 + 16s + 12s2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + 1.333333333s + s2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + 1.333333333s + 0.4166666667 + s2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + 1.333333333s + s2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + 1.333333333s + s2 = 0 + 0.4166666667 1.333333333s + s2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 1.333333333s + s2 = 0.4166666667 The s term is 1.333333333s. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333s + 0.4444444442 + s2 = 0.4166666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333s + s2 = 0.4166666667 + 0.4444444442 Combine like terms: 0.4166666667 + 0.4444444442 = 0.8611111109 0.4444444442 + 1.333333333s + s2 = 0.8611111109 Factor a perfect square on the left side: (s + 0.6666666665)(s + 0.6666666665) = 0.8611111109 Calculate the square root of the right side: 0.927960727 Break this problem into two subproblems by setting (s + 0.6666666665) equal to 0.927960727 and -0.927960727.

Subproblem 1

s + 0.6666666665 = 0.927960727 Simplifying s + 0.6666666665 = 0.927960727 Reorder the terms: 0.6666666665 + s = 0.927960727 Solving 0.6666666665 + s = 0.927960727 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + s = 0.927960727 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + s = 0.927960727 + -0.6666666665 s = 0.927960727 + -0.6666666665 Combine like terms: 0.927960727 + -0.6666666665 = 0.2612940605 s = 0.2612940605 Simplifying s = 0.2612940605

Subproblem 2

s + 0.6666666665 = -0.927960727 Simplifying s + 0.6666666665 = -0.927960727 Reorder the terms: 0.6666666665 + s = -0.927960727 Solving 0.6666666665 + s = -0.927960727 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + s = -0.927960727 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + s = -0.927960727 + -0.6666666665 s = -0.927960727 + -0.6666666665 Combine like terms: -0.927960727 + -0.6666666665 = -1.5946273935 s = -1.5946273935 Simplifying s = -1.5946273935

Solution

The solution to the problem is based on the solutions from the subproblems. s = {0.2612940605, -1.5946273935}

Solution

s = {0.2612940605, -1.5946273935}

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