154=-4(8+6r)24r

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Solution for 154=-4(8+6r)24r equation:


Simplifying
154 = -4(8 + 6r) * 24r

Reorder the terms for easier multiplication:
154 = -4 * 24r(8 + 6r)

Multiply -4 * 24
154 = -96r(8 + 6r)
154 = (8 * -96r + 6r * -96r)
154 = (-768r + -576r2)

Solving
154 = -768r + -576r2

Solving for variable 'r'.

Reorder the terms:
154 + 768r + 576r2 = -768r + 768r + -576r2 + 576r2

Combine like terms: -768r + 768r = 0
154 + 768r + 576r2 = 0 + -576r2 + 576r2
154 + 768r + 576r2 = -576r2 + 576r2

Combine like terms: -576r2 + 576r2 = 0
154 + 768r + 576r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(77 + 384r + 288r2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(77 + 384r + 288r2)' equal to zero and attempt to solve: Simplifying 77 + 384r + 288r2 = 0 Solving 77 + 384r + 288r2 = 0 Begin completing the square. Divide all terms by 288 the coefficient of the squared term: Divide each side by '288'. 0.2673611111 + 1.333333333r + r2 = 0 Move the constant term to the right: Add '-0.2673611111' to each side of the equation. 0.2673611111 + 1.333333333r + -0.2673611111 + r2 = 0 + -0.2673611111 Reorder the terms: 0.2673611111 + -0.2673611111 + 1.333333333r + r2 = 0 + -0.2673611111 Combine like terms: 0.2673611111 + -0.2673611111 = 0.0000000000 0.0000000000 + 1.333333333r + r2 = 0 + -0.2673611111 1.333333333r + r2 = 0 + -0.2673611111 Combine like terms: 0 + -0.2673611111 = -0.2673611111 1.333333333r + r2 = -0.2673611111 The r term is 1.333333333r. 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. 1.333333333r + 0.4444444442 + r2 = -0.2673611111 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333r + r2 = -0.2673611111 + 0.4444444442 Combine like terms: -0.2673611111 + 0.4444444442 = 0.1770833331 0.4444444442 + 1.333333333r + r2 = 0.1770833331 Factor a perfect square on the left side: (r + 0.6666666665)(r + 0.6666666665) = 0.1770833331 Calculate the square root of the right side: 0.420812705 Break this problem into two subproblems by setting (r + 0.6666666665) equal to 0.420812705 and -0.420812705.

Subproblem 1

r + 0.6666666665 = 0.420812705 Simplifying r + 0.6666666665 = 0.420812705 Reorder the terms: 0.6666666665 + r = 0.420812705 Solving 0.6666666665 + r = 0.420812705 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + r = 0.420812705 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + r = 0.420812705 + -0.6666666665 r = 0.420812705 + -0.6666666665 Combine like terms: 0.420812705 + -0.6666666665 = -0.2458539615 r = -0.2458539615 Simplifying r = -0.2458539615

Subproblem 2

r + 0.6666666665 = -0.420812705 Simplifying r + 0.6666666665 = -0.420812705 Reorder the terms: 0.6666666665 + r = -0.420812705 Solving 0.6666666665 + r = -0.420812705 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + r = -0.420812705 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + r = -0.420812705 + -0.6666666665 r = -0.420812705 + -0.6666666665 Combine like terms: -0.420812705 + -0.6666666665 = -1.0874793715 r = -1.0874793715 Simplifying r = -1.0874793715

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.2458539615, -1.0874793715}

Solution

r = {-0.2458539615, -1.0874793715}

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