5x^2=14x-3

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Solution for 5x^2=14x-3 equation:


Simplifying
5x2 = 14x + -3

Reorder the terms:
5x2 = -3 + 14x

Solving
5x2 = -3 + 14x

Solving for variable 'x'.

Reorder the terms:
3 + -14x + 5x2 = -3 + 14x + 3 + -14x

Reorder the terms:
3 + -14x + 5x2 = -3 + 3 + 14x + -14x

Combine like terms: -3 + 3 = 0
3 + -14x + 5x2 = 0 + 14x + -14x
3 + -14x + 5x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
3 + -14x + 5x2 = 0

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

Divide each side by '5'.
0.6 + -2.8x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -2.8x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -2.8x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -2.8x + x2 = 0 + -0.6
-2.8x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-2.8x + x2 = -0.6

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = -0.6 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = -0.6 + 1.96

Combine like terms: -0.6 + 1.96 = 1.36
1.96 + -2.8x + x2 = 1.36

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 1.36

Calculate the square root of the right side: 1.166190379

Break this problem into two subproblems by setting 
(x + -1.4) equal to 1.166190379 and -1.166190379.

Subproblem 1

x + -1.4 = 1.166190379 Simplifying x + -1.4 = 1.166190379 Reorder the terms: -1.4 + x = 1.166190379 Solving -1.4 + x = 1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 1.166190379 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 1.166190379 + 1.4 x = 1.166190379 + 1.4 Combine like terms: 1.166190379 + 1.4 = 2.566190379 x = 2.566190379 Simplifying x = 2.566190379

Subproblem 2

x + -1.4 = -1.166190379 Simplifying x + -1.4 = -1.166190379 Reorder the terms: -1.4 + x = -1.166190379 Solving -1.4 + x = -1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -1.166190379 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -1.166190379 + 1.4 x = -1.166190379 + 1.4 Combine like terms: -1.166190379 + 1.4 = 0.233809621 x = 0.233809621 Simplifying x = 0.233809621

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.566190379, 0.233809621}

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