4a^2+6a-3=0

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Solution for 4a^2+6a-3=0 equation:


Simplifying
4a2 + 6a + -3 = 0

Reorder the terms:
-3 + 6a + 4a2 = 0

Solving
-3 + 6a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
-0.75 + 1.5a + a2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1.5a + 0.75 + a2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1.5a + a2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1.5a + a2 = 0 + 0.75
1.5a + a2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
1.5a + a2 = 0.75

The a term is 1.5a.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5a + 0.5625 + a2 = 0.75 + 0.5625

Reorder the terms:
0.5625 + 1.5a + a2 = 0.75 + 0.5625

Combine like terms: 0.75 + 0.5625 = 1.3125
0.5625 + 1.5a + a2 = 1.3125

Factor a perfect square on the left side:
(a + 0.75)(a + 0.75) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(a + 0.75) equal to 1.145643924 and -1.145643924.

Subproblem 1

a + 0.75 = 1.145643924 Simplifying a + 0.75 = 1.145643924 Reorder the terms: 0.75 + a = 1.145643924 Solving 0.75 + a = 1.145643924 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = 1.145643924 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 1.145643924 + -0.75 a = 1.145643924 + -0.75 Combine like terms: 1.145643924 + -0.75 = 0.395643924 a = 0.395643924 Simplifying a = 0.395643924

Subproblem 2

a + 0.75 = -1.145643924 Simplifying a + 0.75 = -1.145643924 Reorder the terms: 0.75 + a = -1.145643924 Solving 0.75 + a = -1.145643924 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = -1.145643924 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -1.145643924 + -0.75 a = -1.145643924 + -0.75 Combine like terms: -1.145643924 + -0.75 = -1.895643924 a = -1.895643924 Simplifying a = -1.895643924

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.395643924, -1.895643924}

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