2x^2-147x+49=0

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Solution for 2x^2-147x+49=0 equation:


Simplifying
2x2 + -147x + 49 = 0

Reorder the terms:
49 + -147x + 2x2 = 0

Solving
49 + -147x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
24.5 + -73.5x + x2 = 0

Move the constant term to the right:

Add '-24.5' to each side of the equation.
24.5 + -73.5x + -24.5 + x2 = 0 + -24.5

Reorder the terms:
24.5 + -24.5 + -73.5x + x2 = 0 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
0.0 + -73.5x + x2 = 0 + -24.5
-73.5x + x2 = 0 + -24.5

Combine like terms: 0 + -24.5 = -24.5
-73.5x + x2 = -24.5

The x term is -73.5x.  Take half its coefficient (-36.75).
Square it (1350.5625) and add it to both sides.

Add '1350.5625' to each side of the equation.
-73.5x + 1350.5625 + x2 = -24.5 + 1350.5625

Reorder the terms:
1350.5625 + -73.5x + x2 = -24.5 + 1350.5625

Combine like terms: -24.5 + 1350.5625 = 1326.0625
1350.5625 + -73.5x + x2 = 1326.0625

Factor a perfect square on the left side:
(x + -36.75)(x + -36.75) = 1326.0625

Calculate the square root of the right side: 36.415141082

Break this problem into two subproblems by setting 
(x + -36.75) equal to 36.415141082 and -36.415141082.

Subproblem 1

x + -36.75 = 36.415141082 Simplifying x + -36.75 = 36.415141082 Reorder the terms: -36.75 + x = 36.415141082 Solving -36.75 + x = 36.415141082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.75' to each side of the equation. -36.75 + 36.75 + x = 36.415141082 + 36.75 Combine like terms: -36.75 + 36.75 = 0.00 0.00 + x = 36.415141082 + 36.75 x = 36.415141082 + 36.75 Combine like terms: 36.415141082 + 36.75 = 73.165141082 x = 73.165141082 Simplifying x = 73.165141082

Subproblem 2

x + -36.75 = -36.415141082 Simplifying x + -36.75 = -36.415141082 Reorder the terms: -36.75 + x = -36.415141082 Solving -36.75 + x = -36.415141082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.75' to each side of the equation. -36.75 + 36.75 + x = -36.415141082 + 36.75 Combine like terms: -36.75 + 36.75 = 0.00 0.00 + x = -36.415141082 + 36.75 x = -36.415141082 + 36.75 Combine like terms: -36.415141082 + 36.75 = 0.334858918 x = 0.334858918 Simplifying x = 0.334858918

Solution

The solution to the problem is based on the solutions from the subproblems. x = {73.165141082, 0.334858918}

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