49x^2-392x+450=0

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Solution for 49x^2-392x+450=0 equation:


Simplifying
49x2 + -392x + 450 = 0

Reorder the terms:
450 + -392x + 49x2 = 0

Solving
450 + -392x + 49x2 = 0

Solving for variable 'x'.

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

Divide each side by '49'.
9.183673469 + -8x + x2 = 0

Move the constant term to the right:

Add '-9.183673469' to each side of the equation.
9.183673469 + -8x + -9.183673469 + x2 = 0 + -9.183673469

Reorder the terms:
9.183673469 + -9.183673469 + -8x + x2 = 0 + -9.183673469

Combine like terms: 9.183673469 + -9.183673469 = 0.000000000
0.000000000 + -8x + x2 = 0 + -9.183673469
-8x + x2 = 0 + -9.183673469

Combine like terms: 0 + -9.183673469 = -9.183673469
-8x + x2 = -9.183673469

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 = -9.183673469 + 16

Reorder the terms:
16 + -8x + x2 = -9.183673469 + 16

Combine like terms: -9.183673469 + 16 = 6.816326531
16 + -8x + x2 = 6.816326531

Factor a perfect square on the left side:
(x + -4)(x + -4) = 6.816326531

Calculate the square root of the right side: 2.610809555

Break this problem into two subproblems by setting 
(x + -4) equal to 2.610809555 and -2.610809555.

Subproblem 1

x + -4 = 2.610809555 Simplifying x + -4 = 2.610809555 Reorder the terms: -4 + x = 2.610809555 Solving -4 + x = 2.610809555 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 = 2.610809555 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.610809555 + 4 x = 2.610809555 + 4 Combine like terms: 2.610809555 + 4 = 6.610809555 x = 6.610809555 Simplifying x = 6.610809555

Subproblem 2

x + -4 = -2.610809555 Simplifying x + -4 = -2.610809555 Reorder the terms: -4 + x = -2.610809555 Solving -4 + x = -2.610809555 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 = -2.610809555 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.610809555 + 4 x = -2.610809555 + 4 Combine like terms: -2.610809555 + 4 = 1.389190445 x = 1.389190445 Simplifying x = 1.389190445

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.610809555, 1.389190445}

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