6r^2+21r-21=

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Solution for 6r^2+21r-21= equation:


Simplifying
6r2 + 21r + -21 = 0

Reorder the terms:
-21 + 21r + 6r2 = 0

Solving
-21 + 21r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 7r + 2r2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-7 + 7r + 2r2)' equal to zero and attempt to solve: Simplifying -7 + 7r + 2r2 = 0 Solving -7 + 7r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 3.5r + r2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 3.5r + 3.5 + r2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 3.5r + r2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 3.5r + r2 = 0 + 3.5 3.5r + r2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 3.5r + r2 = 3.5 The r term is 3.5r. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5r + 3.0625 + r2 = 3.5 + 3.0625 Reorder the terms: 3.0625 + 3.5r + r2 = 3.5 + 3.0625 Combine like terms: 3.5 + 3.0625 = 6.5625 3.0625 + 3.5r + r2 = 6.5625 Factor a perfect square on the left side: (r + 1.75)(r + 1.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (r + 1.75) equal to 2.561737691 and -2.561737691.

Subproblem 1

r + 1.75 = 2.561737691 Simplifying r + 1.75 = 2.561737691 Reorder the terms: 1.75 + r = 2.561737691 Solving 1.75 + r = 2.561737691 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + r = 2.561737691 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + r = 2.561737691 + -1.75 r = 2.561737691 + -1.75 Combine like terms: 2.561737691 + -1.75 = 0.811737691 r = 0.811737691 Simplifying r = 0.811737691

Subproblem 2

r + 1.75 = -2.561737691 Simplifying r + 1.75 = -2.561737691 Reorder the terms: 1.75 + r = -2.561737691 Solving 1.75 + r = -2.561737691 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + r = -2.561737691 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + r = -2.561737691 + -1.75 r = -2.561737691 + -1.75 Combine like terms: -2.561737691 + -1.75 = -4.311737691 r = -4.311737691 Simplifying r = -4.311737691

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.811737691, -4.311737691}

Solution

r = {0.811737691, -4.311737691}

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