4a^2+5a-8=0

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Solution for 4a^2+5a-8=0 equation:


Simplifying
4a2 + 5a + -8 = 0

Reorder the terms:
-8 + 5a + 4a2 = 0

Solving
-8 + 5a + 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'.
-2 + 1.25a + a2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.25a + 2 + a2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.25a + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.25a + a2 = 0 + 2
1.25a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.25a + a2 = 2

The a term is 1.25a.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25a + 0.390625 + a2 = 2 + 0.390625

Reorder the terms:
0.390625 + 1.25a + a2 = 2 + 0.390625

Combine like terms: 2 + 0.390625 = 2.390625
0.390625 + 1.25a + a2 = 2.390625

Factor a perfect square on the left side:
(a + 0.625)(a + 0.625) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(a + 0.625) equal to 1.54616461 and -1.54616461.

Subproblem 1

a + 0.625 = 1.54616461 Simplifying a + 0.625 = 1.54616461 Reorder the terms: 0.625 + a = 1.54616461 Solving 0.625 + a = 1.54616461 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + a = 1.54616461 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + a = 1.54616461 + -0.625 a = 1.54616461 + -0.625 Combine like terms: 1.54616461 + -0.625 = 0.92116461 a = 0.92116461 Simplifying a = 0.92116461

Subproblem 2

a + 0.625 = -1.54616461 Simplifying a + 0.625 = -1.54616461 Reorder the terms: 0.625 + a = -1.54616461 Solving 0.625 + a = -1.54616461 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + a = -1.54616461 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + a = -1.54616461 + -0.625 a = -1.54616461 + -0.625 Combine like terms: -1.54616461 + -0.625 = -2.17116461 a = -2.17116461 Simplifying a = -2.17116461

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.92116461, -2.17116461}

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