2x^2-2=7x

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


Simplifying
2x2 + -2 = 7x

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

Solving
-2 + 2x2 = 7x

Solving for variable 'x'.

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

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

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

Divide each side by '2'.
-1 + -3.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3.5x + x2 = 0 + 1
-3.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3.5x + x2 = 1

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 = 1 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 1 + 3.0625

Combine like terms: 1 + 3.0625 = 4.0625
3.0625 + -3.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.015564437 and -2.015564437.

Subproblem 1

x + -1.75 = 2.015564437 Simplifying x + -1.75 = 2.015564437 Reorder the terms: -1.75 + x = 2.015564437 Solving -1.75 + x = 2.015564437 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 = 2.015564437 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.015564437 + 1.75 x = 2.015564437 + 1.75 Combine like terms: 2.015564437 + 1.75 = 3.765564437 x = 3.765564437 Simplifying x = 3.765564437

Subproblem 2

x + -1.75 = -2.015564437 Simplifying x + -1.75 = -2.015564437 Reorder the terms: -1.75 + x = -2.015564437 Solving -1.75 + x = -2.015564437 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 = -2.015564437 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.015564437 + 1.75 x = -2.015564437 + 1.75 Combine like terms: -2.015564437 + 1.75 = -0.265564437 x = -0.265564437 Simplifying x = -0.265564437

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.765564437, -0.265564437}

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