4x^2-28x+7=0

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Solution for 4x^2-28x+7=0 equation:


Simplifying
4x2 + -28x + 7 = 0

Reorder the terms:
7 + -28x + 4x2 = 0

Solving
7 + -28x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
1.75 + -7x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -7x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -7x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -7x + x2 = 0 + -1.75
-7x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-7x + x2 = -1.75

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -1.75 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -1.75 + 12.25

Combine like terms: -1.75 + 12.25 = 10.5
12.25 + -7x + x2 = 10.5

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 10.5

Calculate the square root of the right side: 3.240370349

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.240370349 and -3.240370349.

Subproblem 1

x + -3.5 = 3.240370349 Simplifying x + -3.5 = 3.240370349 Reorder the terms: -3.5 + x = 3.240370349 Solving -3.5 + x = 3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.240370349 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.240370349 + 3.5 x = 3.240370349 + 3.5 Combine like terms: 3.240370349 + 3.5 = 6.740370349 x = 6.740370349 Simplifying x = 6.740370349

Subproblem 2

x + -3.5 = -3.240370349 Simplifying x + -3.5 = -3.240370349 Reorder the terms: -3.5 + x = -3.240370349 Solving -3.5 + x = -3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.240370349 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.240370349 + 3.5 x = -3.240370349 + 3.5 Combine like terms: -3.240370349 + 3.5 = 0.259629651 x = 0.259629651 Simplifying x = 0.259629651

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.740370349, 0.259629651}

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