2x^2-10x=7

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Solution for 2x^2-10x=7 equation:


Simplifying
2x2 + -10x = 7

Reorder the terms:
-10x + 2x2 = 7

Solving
-10x + 2x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + -10x + 2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -10x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + -5x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -5x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -5x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -5x + x2 = 0 + 3.5
-5x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-5x + x2 = 3.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 3.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 3.5 + 6.25

Combine like terms: 3.5 + 6.25 = 9.75
6.25 + -5x + x2 = 9.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.122498999 and -3.122498999.

Subproblem 1

x + -2.5 = 3.122498999 Simplifying x + -2.5 = 3.122498999 Reorder the terms: -2.5 + x = 3.122498999 Solving -2.5 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.122498999 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.122498999 + 2.5 x = 3.122498999 + 2.5 Combine like terms: 3.122498999 + 2.5 = 5.622498999 x = 5.622498999 Simplifying x = 5.622498999

Subproblem 2

x + -2.5 = -3.122498999 Simplifying x + -2.5 = -3.122498999 Reorder the terms: -2.5 + x = -3.122498999 Solving -2.5 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.122498999 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.122498999 + 2.5 x = -3.122498999 + 2.5 Combine like terms: -3.122498999 + 2.5 = -0.622498999 x = -0.622498999 Simplifying x = -0.622498999

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.622498999, -0.622498999}

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