5r^2+12r-7=0

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Solution for 5r^2+12r-7=0 equation:


Simplifying
5r2 + 12r + -7 = 0

Reorder the terms:
-7 + 12r + 5r2 = 0

Solving
-7 + 12r + 5r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-1.4 + 2.4r + r2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 2.4r + 1.4 + r2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 2.4r + r2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 2.4r + r2 = 0 + 1.4
2.4r + r2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
2.4r + r2 = 1.4

The r term is 2.4r.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4r + 1.44 + r2 = 1.4 + 1.44

Reorder the terms:
1.44 + 2.4r + r2 = 1.4 + 1.44

Combine like terms: 1.4 + 1.44 = 2.84
1.44 + 2.4r + r2 = 2.84

Factor a perfect square on the left side:
(r + 1.2)(r + 1.2) = 2.84

Calculate the square root of the right side: 1.685229955

Break this problem into two subproblems by setting 
(r + 1.2) equal to 1.685229955 and -1.685229955.

Subproblem 1

r + 1.2 = 1.685229955 Simplifying r + 1.2 = 1.685229955 Reorder the terms: 1.2 + r = 1.685229955 Solving 1.2 + r = 1.685229955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + r = 1.685229955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + r = 1.685229955 + -1.2 r = 1.685229955 + -1.2 Combine like terms: 1.685229955 + -1.2 = 0.485229955 r = 0.485229955 Simplifying r = 0.485229955

Subproblem 2

r + 1.2 = -1.685229955 Simplifying r + 1.2 = -1.685229955 Reorder the terms: 1.2 + r = -1.685229955 Solving 1.2 + r = -1.685229955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + r = -1.685229955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + r = -1.685229955 + -1.2 r = -1.685229955 + -1.2 Combine like terms: -1.685229955 + -1.2 = -2.885229955 r = -2.885229955 Simplifying r = -2.885229955

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.485229955, -2.885229955}

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