7a^2+12a-11=0

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Solution for 7a^2+12a-11=0 equation:


Simplifying
7a2 + 12a + -11 = 0

Reorder the terms:
-11 + 12a + 7a2 = 0

Solving
-11 + 12a + 7a2 = 0

Solving for variable 'a'.

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

Divide each side by '7'.
-1.571428571 + 1.714285714a + a2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + 1.714285714a + 1.571428571 + a2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + 1.714285714a + a2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + 1.714285714a + a2 = 0 + 1.571428571
1.714285714a + a2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
1.714285714a + a2 = 1.571428571

The a term is 1.714285714a.  Take half its coefficient (0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
1.714285714a + 0.7346938773 + a2 = 1.571428571 + 0.7346938773

Reorder the terms:
0.7346938773 + 1.714285714a + a2 = 1.571428571 + 0.7346938773

Combine like terms: 1.571428571 + 0.7346938773 = 2.3061224483
0.7346938773 + 1.714285714a + a2 = 2.3061224483

Factor a perfect square on the left side:
(a + 0.857142857)(a + 0.857142857) = 2.3061224483

Calculate the square root of the right side: 1.518592259

Break this problem into two subproblems by setting 
(a + 0.857142857) equal to 1.518592259 and -1.518592259.

Subproblem 1

a + 0.857142857 = 1.518592259 Simplifying a + 0.857142857 = 1.518592259 Reorder the terms: 0.857142857 + a = 1.518592259 Solving 0.857142857 + a = 1.518592259 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + a = 1.518592259 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + a = 1.518592259 + -0.857142857 a = 1.518592259 + -0.857142857 Combine like terms: 1.518592259 + -0.857142857 = 0.661449402 a = 0.661449402 Simplifying a = 0.661449402

Subproblem 2

a + 0.857142857 = -1.518592259 Simplifying a + 0.857142857 = -1.518592259 Reorder the terms: 0.857142857 + a = -1.518592259 Solving 0.857142857 + a = -1.518592259 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + a = -1.518592259 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + a = -1.518592259 + -0.857142857 a = -1.518592259 + -0.857142857 Combine like terms: -1.518592259 + -0.857142857 = -2.375735116 a = -2.375735116 Simplifying a = -2.375735116

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.661449402, -2.375735116}

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