2a^2+3a-7=200

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Solution for 2a^2+3a-7=200 equation:


Simplifying
2a2 + 3a + -7 = 200

Reorder the terms:
-7 + 3a + 2a2 = 200

Solving
-7 + 3a + 2a2 = 200

Solving for variable 'a'.

Reorder the terms:
-7 + -200 + 3a + 2a2 = 200 + -200

Combine like terms: -7 + -200 = -207
-207 + 3a + 2a2 = 200 + -200

Combine like terms: 200 + -200 = 0
-207 + 3a + 2a2 = 0

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

Divide each side by '2'.
-103.5 + 1.5a + a2 = 0

Move the constant term to the right:

Add '103.5' to each side of the equation.
-103.5 + 1.5a + 103.5 + a2 = 0 + 103.5

Reorder the terms:
-103.5 + 103.5 + 1.5a + a2 = 0 + 103.5

Combine like terms: -103.5 + 103.5 = 0.0
0.0 + 1.5a + a2 = 0 + 103.5
1.5a + a2 = 0 + 103.5

Combine like terms: 0 + 103.5 = 103.5
1.5a + a2 = 103.5

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 = 103.5 + 0.5625

Reorder the terms:
0.5625 + 1.5a + a2 = 103.5 + 0.5625

Combine like terms: 103.5 + 0.5625 = 104.0625
0.5625 + 1.5a + a2 = 104.0625

Factor a perfect square on the left side:
(a + 0.75)(a + 0.75) = 104.0625

Calculate the square root of the right side: 10.201102882

Break this problem into two subproblems by setting 
(a + 0.75) equal to 10.201102882 and -10.201102882.

Subproblem 1

a + 0.75 = 10.201102882 Simplifying a + 0.75 = 10.201102882 Reorder the terms: 0.75 + a = 10.201102882 Solving 0.75 + a = 10.201102882 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 = 10.201102882 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 10.201102882 + -0.75 a = 10.201102882 + -0.75 Combine like terms: 10.201102882 + -0.75 = 9.451102882 a = 9.451102882 Simplifying a = 9.451102882

Subproblem 2

a + 0.75 = -10.201102882 Simplifying a + 0.75 = -10.201102882 Reorder the terms: 0.75 + a = -10.201102882 Solving 0.75 + a = -10.201102882 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 = -10.201102882 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -10.201102882 + -0.75 a = -10.201102882 + -0.75 Combine like terms: -10.201102882 + -0.75 = -10.951102882 a = -10.951102882 Simplifying a = -10.951102882

Solution

The solution to the problem is based on the solutions from the subproblems. a = {9.451102882, -10.951102882}

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