4x^2-28x+43=0

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Solution for 4x^2-28x+43=0 equation:


Simplifying
4x2 + -28x + 43 = 0

Reorder the terms:
43 + -28x + 4x2 = 0

Solving
43 + -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'.
10.75 + -7x + x2 = 0

Move the constant term to the right:

Add '-10.75' to each side of the equation.
10.75 + -7x + -10.75 + x2 = 0 + -10.75

Reorder the terms:
10.75 + -10.75 + -7x + x2 = 0 + -10.75

Combine like terms: 10.75 + -10.75 = 0.00
0.00 + -7x + x2 = 0 + -10.75
-7x + x2 = 0 + -10.75

Combine like terms: 0 + -10.75 = -10.75
-7x + x2 = -10.75

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 = -10.75 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -10.75 + 12.25

Combine like terms: -10.75 + 12.25 = 1.5
12.25 + -7x + x2 = 1.5

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + -3.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

x + -3.5 = 1.224744871 Simplifying x + -3.5 = 1.224744871 Reorder the terms: -3.5 + x = 1.224744871 Solving -3.5 + x = 1.224744871 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 = 1.224744871 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.224744871 + 3.5 x = 1.224744871 + 3.5 Combine like terms: 1.224744871 + 3.5 = 4.724744871 x = 4.724744871 Simplifying x = 4.724744871

Subproblem 2

x + -3.5 = -1.224744871 Simplifying x + -3.5 = -1.224744871 Reorder the terms: -3.5 + x = -1.224744871 Solving -3.5 + x = -1.224744871 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 = -1.224744871 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.224744871 + 3.5 x = -1.224744871 + 3.5 Combine like terms: -1.224744871 + 3.5 = 2.275255129 x = 2.275255129 Simplifying x = 2.275255129

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.724744871, 2.275255129}

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