2a^2+3a-7=55

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Solution for 2a^2+3a-7=55 equation:


Simplifying
2a2 + 3a + -7 = 55

Reorder the terms:
-7 + 3a + 2a2 = 55

Solving
-7 + 3a + 2a2 = 55

Solving for variable 'a'.

Reorder the terms:
-7 + -55 + 3a + 2a2 = 55 + -55

Combine like terms: -7 + -55 = -62
-62 + 3a + 2a2 = 55 + -55

Combine like terms: 55 + -55 = 0
-62 + 3a + 2a2 = 0

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

Divide each side by '2'.
-31 + 1.5a + a2 = 0

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 1.5a + 31 + a2 = 0 + 31

Reorder the terms:
-31 + 31 + 1.5a + a2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 1.5a + a2 = 0 + 31
1.5a + a2 = 0 + 31

Combine like terms: 0 + 31 = 31
1.5a + a2 = 31

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 = 31 + 0.5625

Reorder the terms:
0.5625 + 1.5a + a2 = 31 + 0.5625

Combine like terms: 31 + 0.5625 = 31.5625
0.5625 + 1.5a + a2 = 31.5625

Factor a perfect square on the left side:
(a + 0.75)(a + 0.75) = 31.5625

Calculate the square root of the right side: 5.618051264

Break this problem into two subproblems by setting 
(a + 0.75) equal to 5.618051264 and -5.618051264.

Subproblem 1

a + 0.75 = 5.618051264 Simplifying a + 0.75 = 5.618051264 Reorder the terms: 0.75 + a = 5.618051264 Solving 0.75 + a = 5.618051264 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 = 5.618051264 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 5.618051264 + -0.75 a = 5.618051264 + -0.75 Combine like terms: 5.618051264 + -0.75 = 4.868051264 a = 4.868051264 Simplifying a = 4.868051264

Subproblem 2

a + 0.75 = -5.618051264 Simplifying a + 0.75 = -5.618051264 Reorder the terms: 0.75 + a = -5.618051264 Solving 0.75 + a = -5.618051264 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 = -5.618051264 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -5.618051264 + -0.75 a = -5.618051264 + -0.75 Combine like terms: -5.618051264 + -0.75 = -6.368051264 a = -6.368051264 Simplifying a = -6.368051264

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.868051264, -6.368051264}

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