a+a^2=0.24

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Solution for a+a^2=0.24 equation:


Simplifying
a + a2 = 0.24

Solving
a + a2 = 0.24

Solving for variable 'a'.

Reorder the terms:
-0.24 + a + a2 = 0.24 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
-0.24 + a + a2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.24' to each side of the equation.
-0.24 + a + 0.24 + a2 = 0.00 + 0.24

Reorder the terms:
-0.24 + 0.24 + a + a2 = 0.00 + 0.24

Combine like terms: -0.24 + 0.24 = 0.00
0.00 + a + a2 = 0.00 + 0.24
a + a2 = 0.00 + 0.24

Combine like terms: 0.00 + 0.24 = 0.24
a + a2 = 0.24

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.
a + 0.25 + a2 = 0.24 + 0.25

Reorder the terms:
0.25 + a + a2 = 0.24 + 0.25

Combine like terms: 0.24 + 0.25 = 0.49
0.25 + a + a2 = 0.49

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 0.49

Calculate the square root of the right side: 0.7

Break this problem into two subproblems by setting 
(a + 0.5) equal to 0.7 and -0.7.

Subproblem 1

a + 0.5 = 0.7 Simplifying a + 0.5 = 0.7 Reorder the terms: 0.5 + a = 0.7 Solving 0.5 + a = 0.7 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 = 0.7 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 0.7 + -0.5 a = 0.7 + -0.5 Combine like terms: 0.7 + -0.5 = 0.2 a = 0.2 Simplifying a = 0.2

Subproblem 2

a + 0.5 = -0.7 Simplifying a + 0.5 = -0.7 Reorder the terms: 0.5 + a = -0.7 Solving 0.5 + a = -0.7 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 = -0.7 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -0.7 + -0.5 a = -0.7 + -0.5 Combine like terms: -0.7 + -0.5 = -1.2 a = -1.2 Simplifying a = -1.2

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.2, -1.2}

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