4x^2=14x+5

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Solution for 4x^2=14x+5 equation:


Simplifying
4x2 = 14x + 5

Reorder the terms:
4x2 = 5 + 14x

Solving
4x2 = 5 + 14x

Solving for variable 'x'.

Reorder the terms:
-5 + -14x + 4x2 = 5 + 14x + -5 + -14x

Reorder the terms:
-5 + -14x + 4x2 = 5 + -5 + 14x + -14x

Combine like terms: 5 + -5 = 0
-5 + -14x + 4x2 = 0 + 14x + -14x
-5 + -14x + 4x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-5 + -14x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + -3.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -3.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -3.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -3.5x + x2 = 0 + 1.25
-3.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-3.5x + x2 = 1.25

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 1.25 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 1.25 + 3.0625

Combine like terms: 1.25 + 3.0625 = 4.3125
3.0625 + -3.5x + x2 = 4.3125

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.076655966 and -2.076655966.

Subproblem 1

x + -1.75 = 2.076655966 Simplifying x + -1.75 = 2.076655966 Reorder the terms: -1.75 + x = 2.076655966 Solving -1.75 + x = 2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.076655966 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.076655966 + 1.75 x = 2.076655966 + 1.75 Combine like terms: 2.076655966 + 1.75 = 3.826655966 x = 3.826655966 Simplifying x = 3.826655966

Subproblem 2

x + -1.75 = -2.076655966 Simplifying x + -1.75 = -2.076655966 Reorder the terms: -1.75 + x = -2.076655966 Solving -1.75 + x = -2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.076655966 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.076655966 + 1.75 x = -2.076655966 + 1.75 Combine like terms: -2.076655966 + 1.75 = -0.326655966 x = -0.326655966 Simplifying x = -0.326655966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.826655966, -0.326655966}

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