26x^2-49x+16=

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Solution for 26x^2-49x+16= equation:


Simplifying
26x2 + -49x + 16 = 0

Reorder the terms:
16 + -49x + 26x2 = 0

Solving
16 + -49x + 26x2 = 0

Solving for variable 'x'.

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

Divide each side by '26'.
0.6153846154 + -1.884615385x + x2 = 0

Move the constant term to the right:

Add '-0.6153846154' to each side of the equation.
0.6153846154 + -1.884615385x + -0.6153846154 + x2 = 0 + -0.6153846154

Reorder the terms:
0.6153846154 + -0.6153846154 + -1.884615385x + x2 = 0 + -0.6153846154

Combine like terms: 0.6153846154 + -0.6153846154 = 0.0000000000
0.0000000000 + -1.884615385x + x2 = 0 + -0.6153846154
-1.884615385x + x2 = 0 + -0.6153846154

Combine like terms: 0 + -0.6153846154 = -0.6153846154
-1.884615385x + x2 = -0.6153846154

The x term is -1.884615385x.  Take half its coefficient (-0.9423076925).
Square it (0.8879437873) and add it to both sides.

Add '0.8879437873' to each side of the equation.
-1.884615385x + 0.8879437873 + x2 = -0.6153846154 + 0.8879437873

Reorder the terms:
0.8879437873 + -1.884615385x + x2 = -0.6153846154 + 0.8879437873

Combine like terms: -0.6153846154 + 0.8879437873 = 0.2725591719
0.8879437873 + -1.884615385x + x2 = 0.2725591719

Factor a perfect square on the left side:
(x + -0.9423076925)(x + -0.9423076925) = 0.2725591719

Calculate the square root of the right side: 0.522071999

Break this problem into two subproblems by setting 
(x + -0.9423076925) equal to 0.522071999 and -0.522071999.

Subproblem 1

x + -0.9423076925 = 0.522071999 Simplifying x + -0.9423076925 = 0.522071999 Reorder the terms: -0.9423076925 + x = 0.522071999 Solving -0.9423076925 + x = 0.522071999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9423076925' to each side of the equation. -0.9423076925 + 0.9423076925 + x = 0.522071999 + 0.9423076925 Combine like terms: -0.9423076925 + 0.9423076925 = 0.0000000000 0.0000000000 + x = 0.522071999 + 0.9423076925 x = 0.522071999 + 0.9423076925 Combine like terms: 0.522071999 + 0.9423076925 = 1.4643796915 x = 1.4643796915 Simplifying x = 1.4643796915

Subproblem 2

x + -0.9423076925 = -0.522071999 Simplifying x + -0.9423076925 = -0.522071999 Reorder the terms: -0.9423076925 + x = -0.522071999 Solving -0.9423076925 + x = -0.522071999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9423076925' to each side of the equation. -0.9423076925 + 0.9423076925 + x = -0.522071999 + 0.9423076925 Combine like terms: -0.9423076925 + 0.9423076925 = 0.0000000000 0.0000000000 + x = -0.522071999 + 0.9423076925 x = -0.522071999 + 0.9423076925 Combine like terms: -0.522071999 + 0.9423076925 = 0.4202356935 x = 0.4202356935 Simplifying x = 0.4202356935

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4643796915, 0.4202356935}

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