4a^2+a-15=

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Solution for 4a^2+a-15= equation:


Simplifying
4a2 + a + -15 = 0

Reorder the terms:
-15 + a + 4a2 = 0

Solving
-15 + a + 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'.
-3.75 + 0.25a + a2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 0.25a + 3.75 + a2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 0.25a + a2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 0.25a + a2 = 0 + 3.75
0.25a + a2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
0.25a + a2 = 3.75

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25a + 0.25 + a2 = 3.75 + 0.25

Reorder the terms:
0.25 + 0.25a + a2 = 3.75 + 0.25

Combine like terms: 3.75 + 0.25 = 4
0.25 + 0.25a + a2 = 4

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(a + 0.5) equal to 2 and -2.

Subproblem 1

a + 0.5 = 2 Simplifying a + 0.5 = 2 Reorder the terms: 0.5 + a = 2 Solving 0.5 + a = 2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 2 + -0.5 a = 2 + -0.5 Combine like terms: 2 + -0.5 = 1.5 a = 1.5 Simplifying a = 1.5

Subproblem 2

a + 0.5 = -2 Simplifying a + 0.5 = -2 Reorder the terms: 0.5 + a = -2 Solving 0.5 + a = -2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -2 + -0.5 a = -2 + -0.5 Combine like terms: -2 + -0.5 = -2.5 a = -2.5 Simplifying a = -2.5

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.5, -2.5}

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