2x^2-16x=7

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Solution for 2x^2-16x=7 equation:


Simplifying
2x2 + -16x = 7

Reorder the terms:
-16x + 2x2 = 7

Solving
-16x + 2x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + -16x + 2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -16x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + -8x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -8x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -8x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -8x + x2 = 0 + 3.5
-8x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-8x + x2 = 3.5

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 3.5 + 16

Reorder the terms:
16 + -8x + x2 = 3.5 + 16

Combine like terms: 3.5 + 16 = 19.5
16 + -8x + x2 = 19.5

Factor a perfect square on the left side:
(x + -4)(x + -4) = 19.5

Calculate the square root of the right side: 4.415880433

Break this problem into two subproblems by setting 
(x + -4) equal to 4.415880433 and -4.415880433.

Subproblem 1

x + -4 = 4.415880433 Simplifying x + -4 = 4.415880433 Reorder the terms: -4 + x = 4.415880433 Solving -4 + x = 4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.415880433 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.415880433 + 4 x = 4.415880433 + 4 Combine like terms: 4.415880433 + 4 = 8.415880433 x = 8.415880433 Simplifying x = 8.415880433

Subproblem 2

x + -4 = -4.415880433 Simplifying x + -4 = -4.415880433 Reorder the terms: -4 + x = -4.415880433 Solving -4 + x = -4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.415880433 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.415880433 + 4 x = -4.415880433 + 4 Combine like terms: -4.415880433 + 4 = -0.415880433 x = -0.415880433 Simplifying x = -0.415880433

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.415880433, -0.415880433}

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