4a^2-23a+5=144

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Solution for 4a^2-23a+5=144 equation:


Simplifying
4a2 + -23a + 5 = 144

Reorder the terms:
5 + -23a + 4a2 = 144

Solving
5 + -23a + 4a2 = 144

Solving for variable 'a'.

Reorder the terms:
5 + -144 + -23a + 4a2 = 144 + -144

Combine like terms: 5 + -144 = -139
-139 + -23a + 4a2 = 144 + -144

Combine like terms: 144 + -144 = 0
-139 + -23a + 4a2 = 0

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

Divide each side by '4'.
-34.75 + -5.75a + a2 = 0

Move the constant term to the right:

Add '34.75' to each side of the equation.
-34.75 + -5.75a + 34.75 + a2 = 0 + 34.75

Reorder the terms:
-34.75 + 34.75 + -5.75a + a2 = 0 + 34.75

Combine like terms: -34.75 + 34.75 = 0.00
0.00 + -5.75a + a2 = 0 + 34.75
-5.75a + a2 = 0 + 34.75

Combine like terms: 0 + 34.75 = 34.75
-5.75a + a2 = 34.75

The a term is -5.75a.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75a + 8.265625 + a2 = 34.75 + 8.265625

Reorder the terms:
8.265625 + -5.75a + a2 = 34.75 + 8.265625

Combine like terms: 34.75 + 8.265625 = 43.015625
8.265625 + -5.75a + a2 = 43.015625

Factor a perfect square on the left side:
(a + -2.875)(a + -2.875) = 43.015625

Calculate the square root of the right side: 6.558629811

Break this problem into two subproblems by setting 
(a + -2.875) equal to 6.558629811 and -6.558629811.

Subproblem 1

a + -2.875 = 6.558629811 Simplifying a + -2.875 = 6.558629811 Reorder the terms: -2.875 + a = 6.558629811 Solving -2.875 + a = 6.558629811 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + a = 6.558629811 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + a = 6.558629811 + 2.875 a = 6.558629811 + 2.875 Combine like terms: 6.558629811 + 2.875 = 9.433629811 a = 9.433629811 Simplifying a = 9.433629811

Subproblem 2

a + -2.875 = -6.558629811 Simplifying a + -2.875 = -6.558629811 Reorder the terms: -2.875 + a = -6.558629811 Solving -2.875 + a = -6.558629811 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + a = -6.558629811 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + a = -6.558629811 + 2.875 a = -6.558629811 + 2.875 Combine like terms: -6.558629811 + 2.875 = -3.683629811 a = -3.683629811 Simplifying a = -3.683629811

Solution

The solution to the problem is based on the solutions from the subproblems. a = {9.433629811, -3.683629811}

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