4x^2-94x+342=03

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Solution for 4x^2-94x+342=03 equation:


Simplifying
4x2 + -94x + 342 = 3

Reorder the terms:
342 + -94x + 4x2 = 3

Solving
342 + -94x + 4x2 = 3

Solving for variable 'x'.

Reorder the terms:
342 + -3 + -94x + 4x2 = 3 + -3

Combine like terms: 342 + -3 = 339
339 + -94x + 4x2 = 3 + -3

Combine like terms: 3 + -3 = 0
339 + -94x + 4x2 = 0

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

Divide each side by '4'.
84.75 + -23.5x + x2 = 0

Move the constant term to the right:

Add '-84.75' to each side of the equation.
84.75 + -23.5x + -84.75 + x2 = 0 + -84.75

Reorder the terms:
84.75 + -84.75 + -23.5x + x2 = 0 + -84.75

Combine like terms: 84.75 + -84.75 = 0.00
0.00 + -23.5x + x2 = 0 + -84.75
-23.5x + x2 = 0 + -84.75

Combine like terms: 0 + -84.75 = -84.75
-23.5x + x2 = -84.75

The x term is -23.5x.  Take half its coefficient (-11.75).
Square it (138.0625) and add it to both sides.

Add '138.0625' to each side of the equation.
-23.5x + 138.0625 + x2 = -84.75 + 138.0625

Reorder the terms:
138.0625 + -23.5x + x2 = -84.75 + 138.0625

Combine like terms: -84.75 + 138.0625 = 53.3125
138.0625 + -23.5x + x2 = 53.3125

Factor a perfect square on the left side:
(x + -11.75)(x + -11.75) = 53.3125

Calculate the square root of the right side: 7.301540933

Break this problem into two subproblems by setting 
(x + -11.75) equal to 7.301540933 and -7.301540933.

Subproblem 1

x + -11.75 = 7.301540933 Simplifying x + -11.75 = 7.301540933 Reorder the terms: -11.75 + x = 7.301540933 Solving -11.75 + x = 7.301540933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = 7.301540933 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = 7.301540933 + 11.75 x = 7.301540933 + 11.75 Combine like terms: 7.301540933 + 11.75 = 19.051540933 x = 19.051540933 Simplifying x = 19.051540933

Subproblem 2

x + -11.75 = -7.301540933 Simplifying x + -11.75 = -7.301540933 Reorder the terms: -11.75 + x = -7.301540933 Solving -11.75 + x = -7.301540933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = -7.301540933 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = -7.301540933 + 11.75 x = -7.301540933 + 11.75 Combine like terms: -7.301540933 + 11.75 = 4.448459067 x = 4.448459067 Simplifying x = 4.448459067

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.051540933, 4.448459067}

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