2x^2-7x=13

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Solution for 2x^2-7x=13 equation:


Simplifying
2x2 + -7x = 13

Reorder the terms:
-7x + 2x2 = 13

Solving
-7x + 2x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + -7x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -7x + 2x2 = 0

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

Divide each side by '2'.
-6.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + -3.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + -3.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + -3.5x + x2 = 0 + 6.5
-3.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
-3.5x + x2 = 6.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 6.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 6.5 + 3.0625

Combine like terms: 6.5 + 3.0625 = 9.5625
3.0625 + -3.5x + x2 = 9.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(x + -1.75) equal to 3.092329219 and -3.092329219.

Subproblem 1

x + -1.75 = 3.092329219 Simplifying x + -1.75 = 3.092329219 Reorder the terms: -1.75 + x = 3.092329219 Solving -1.75 + x = 3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.092329219 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.092329219 + 1.75 x = 3.092329219 + 1.75 Combine like terms: 3.092329219 + 1.75 = 4.842329219 x = 4.842329219 Simplifying x = 4.842329219

Subproblem 2

x + -1.75 = -3.092329219 Simplifying x + -1.75 = -3.092329219 Reorder the terms: -1.75 + x = -3.092329219 Solving -1.75 + x = -3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.092329219 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.092329219 + 1.75 x = -3.092329219 + 1.75 Combine like terms: -3.092329219 + 1.75 = -1.342329219 x = -1.342329219 Simplifying x = -1.342329219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.842329219, -1.342329219}

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