(5x-1)(3x-1)=63

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Solution for (5x-1)(3x-1)=63 equation:


Simplifying
(5x + -1)(3x + -1) = 63

Reorder the terms:
(-1 + 5x)(3x + -1) = 63

Reorder the terms:
(-1 + 5x)(-1 + 3x) = 63

Multiply (-1 + 5x) * (-1 + 3x)
(-1(-1 + 3x) + 5x * (-1 + 3x)) = 63
((-1 * -1 + 3x * -1) + 5x * (-1 + 3x)) = 63
((1 + -3x) + 5x * (-1 + 3x)) = 63
(1 + -3x + (-1 * 5x + 3x * 5x)) = 63
(1 + -3x + (-5x + 15x2)) = 63

Combine like terms: -3x + -5x = -8x
(1 + -8x + 15x2) = 63

Solving
1 + -8x + 15x2 = 63

Solving for variable 'x'.

Reorder the terms:
1 + -63 + -8x + 15x2 = 63 + -63

Combine like terms: 1 + -63 = -62
-62 + -8x + 15x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-62 + -8x + 15x2 = 0

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

Divide each side by '15'.
-4.133333333 + -0.5333333333x + x2 = 0

Move the constant term to the right:

Add '4.133333333' to each side of the equation.
-4.133333333 + -0.5333333333x + 4.133333333 + x2 = 0 + 4.133333333

Reorder the terms:
-4.133333333 + 4.133333333 + -0.5333333333x + x2 = 0 + 4.133333333

Combine like terms: -4.133333333 + 4.133333333 = 0.000000000
0.000000000 + -0.5333333333x + x2 = 0 + 4.133333333
-0.5333333333x + x2 = 0 + 4.133333333

Combine like terms: 0 + 4.133333333 = 4.133333333
-0.5333333333x + x2 = 4.133333333

The x term is -0.5333333333x.  Take half its coefficient (-0.2666666667).
Square it (0.07111111113) and add it to both sides.

Add '0.07111111113' to each side of the equation.
-0.5333333333x + 0.07111111113 + x2 = 4.133333333 + 0.07111111113

Reorder the terms:
0.07111111113 + -0.5333333333x + x2 = 4.133333333 + 0.07111111113

Combine like terms: 4.133333333 + 0.07111111113 = 4.20444444413
0.07111111113 + -0.5333333333x + x2 = 4.20444444413

Factor a perfect square on the left side:
(x + -0.2666666667)(x + -0.2666666667) = 4.20444444413

Calculate the square root of the right side: 2.0504742

Break this problem into two subproblems by setting 
(x + -0.2666666667) equal to 2.0504742 and -2.0504742.

Subproblem 1

x + -0.2666666667 = 2.0504742 Simplifying x + -0.2666666667 = 2.0504742 Reorder the terms: -0.2666666667 + x = 2.0504742 Solving -0.2666666667 + x = 2.0504742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2666666667' to each side of the equation. -0.2666666667 + 0.2666666667 + x = 2.0504742 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + x = 2.0504742 + 0.2666666667 x = 2.0504742 + 0.2666666667 Combine like terms: 2.0504742 + 0.2666666667 = 2.3171408667 x = 2.3171408667 Simplifying x = 2.3171408667

Subproblem 2

x + -0.2666666667 = -2.0504742 Simplifying x + -0.2666666667 = -2.0504742 Reorder the terms: -0.2666666667 + x = -2.0504742 Solving -0.2666666667 + x = -2.0504742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2666666667' to each side of the equation. -0.2666666667 + 0.2666666667 + x = -2.0504742 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + x = -2.0504742 + 0.2666666667 x = -2.0504742 + 0.2666666667 Combine like terms: -2.0504742 + 0.2666666667 = -1.7838075333 x = -1.7838075333 Simplifying x = -1.7838075333

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.3171408667, -1.7838075333}

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