2x^2-16x=-25

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Solution for 2x^2-16x=-25 equation:


Simplifying
2x2 + -16x = -25

Reorder the terms:
-16x + 2x2 = -25

Solving
-16x + 2x2 = -25

Solving for variable 'x'.

Reorder the terms:
25 + -16x + 2x2 = -25 + 25

Combine like terms: -25 + 25 = 0
25 + -16x + 2x2 = 0

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

Divide each side by '2'.
12.5 + -8x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + -8x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + -8x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + -8x + x2 = 0 + -12.5
-8x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
-8x + x2 = -12.5

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 = -12.5 + 16

Reorder the terms:
16 + -8x + x2 = -12.5 + 16

Combine like terms: -12.5 + 16 = 3.5
16 + -8x + x2 = 3.5

Factor a perfect square on the left side:
(x + -4)(x + -4) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(x + -4) equal to 1.870828693 and -1.870828693.

Subproblem 1

x + -4 = 1.870828693 Simplifying x + -4 = 1.870828693 Reorder the terms: -4 + x = 1.870828693 Solving -4 + x = 1.870828693 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 = 1.870828693 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.870828693 + 4 x = 1.870828693 + 4 Combine like terms: 1.870828693 + 4 = 5.870828693 x = 5.870828693 Simplifying x = 5.870828693

Subproblem 2

x + -4 = -1.870828693 Simplifying x + -4 = -1.870828693 Reorder the terms: -4 + x = -1.870828693 Solving -4 + x = -1.870828693 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 = -1.870828693 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.870828693 + 4 x = -1.870828693 + 4 Combine like terms: -1.870828693 + 4 = 2.129171307 x = 2.129171307 Simplifying x = 2.129171307

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.870828693, 2.129171307}

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