4x^2+2x=13

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Solution for 4x^2+2x=13 equation:


Simplifying
4x2 + 2x = 13

Reorder the terms:
2x + 4x2 = 13

Solving
2x + 4x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + 2x + 4x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 2x + 4x2 = 0

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

Divide each side by '4'.
-3.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 0.5x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 0.5x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 0.5x + x2 = 0 + 3.25
0.5x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
0.5x + x2 = 3.25

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 3.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 3.25 + 0.0625

Combine like terms: 3.25 + 0.0625 = 3.3125
0.0625 + 0.5x + x2 = 3.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 3.3125

Calculate the square root of the right side: 1.820027472

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.820027472 and -1.820027472.

Subproblem 1

x + 0.25 = 1.820027472 Simplifying x + 0.25 = 1.820027472 Reorder the terms: 0.25 + x = 1.820027472 Solving 0.25 + x = 1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.820027472 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.820027472 + -0.25 x = 1.820027472 + -0.25 Combine like terms: 1.820027472 + -0.25 = 1.570027472 x = 1.570027472 Simplifying x = 1.570027472

Subproblem 2

x + 0.25 = -1.820027472 Simplifying x + 0.25 = -1.820027472 Reorder the terms: 0.25 + x = -1.820027472 Solving 0.25 + x = -1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.820027472 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.820027472 + -0.25 x = -1.820027472 + -0.25 Combine like terms: -1.820027472 + -0.25 = -2.070027472 x = -2.070027472 Simplifying x = -2.070027472

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.570027472, -2.070027472}

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