2x^2+3x=80

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Solution for 2x^2+3x=80 equation:


Simplifying
2x2 + 3x = 80

Reorder the terms:
3x + 2x2 = 80

Solving
3x + 2x2 = 80

Solving for variable 'x'.

Reorder the terms:
-80 + 3x + 2x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 3x + 2x2 = 0

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

Divide each side by '2'.
-40 + 1.5x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 1.5x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 1.5x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 1.5x + x2 = 0 + 40
1.5x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
1.5x + x2 = 40

The x term is 1.5x.  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.
1.5x + 0.5625 + x2 = 40 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 40 + 0.5625

Combine like terms: 40 + 0.5625 = 40.5625
0.5625 + 1.5x + x2 = 40.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 40.5625

Calculate the square root of the right side: 6.368869601

Break this problem into two subproblems by setting 
(x + 0.75) equal to 6.368869601 and -6.368869601.

Subproblem 1

x + 0.75 = 6.368869601 Simplifying x + 0.75 = 6.368869601 Reorder the terms: 0.75 + x = 6.368869601 Solving 0.75 + x = 6.368869601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 6.368869601 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 6.368869601 + -0.75 x = 6.368869601 + -0.75 Combine like terms: 6.368869601 + -0.75 = 5.618869601 x = 5.618869601 Simplifying x = 5.618869601

Subproblem 2

x + 0.75 = -6.368869601 Simplifying x + 0.75 = -6.368869601 Reorder the terms: 0.75 + x = -6.368869601 Solving 0.75 + x = -6.368869601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -6.368869601 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -6.368869601 + -0.75 x = -6.368869601 + -0.75 Combine like terms: -6.368869601 + -0.75 = -7.118869601 x = -7.118869601 Simplifying x = -7.118869601

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.618869601, -7.118869601}

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