53.0x^2-17.1x+1.14=0

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Solution for 53.0x^2-17.1x+1.14=0 equation:


Simplifying
53.0x2 + -17.1x + 1.14 = 0

Reorder the terms:
1.14 + -17.1x + 53.0x2 = 0

Solving
1.14 + -17.1x + 53.0x2 = 0

Solving for variable 'x'.

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

Divide each side by '53.0'.
0.02150943396 + -0.3226415094x + x2 = 0

Move the constant term to the right:

Add '-0.02150943396' to each side of the equation.
0.02150943396 + -0.3226415094x + -0.02150943396 + x2 = 0 + -0.02150943396

Reorder the terms:
0.02150943396 + -0.02150943396 + -0.3226415094x + x2 = 0 + -0.02150943396

Combine like terms: 0.02150943396 + -0.02150943396 = 0.00000000000
0.00000000000 + -0.3226415094x + x2 = 0 + -0.02150943396
-0.3226415094x + x2 = 0 + -0.02150943396

Combine like terms: 0 + -0.02150943396 = -0.02150943396
-0.3226415094x + x2 = -0.02150943396

The x term is -0.3226415094x.  Take half its coefficient (-0.1613207547).
Square it (0.02602438590) and add it to both sides.

Add '0.02602438590' to each side of the equation.
-0.3226415094x + 0.02602438590 + x2 = -0.02150943396 + 0.02602438590

Reorder the terms:
0.02602438590 + -0.3226415094x + x2 = -0.02150943396 + 0.02602438590

Combine like terms: -0.02150943396 + 0.02602438590 = 0.00451495194
0.02602438590 + -0.3226415094x + x2 = 0.00451495194

Factor a perfect square on the left side:
(x + -0.1613207547)(x + -0.1613207547) = 0.00451495194

Calculate the square root of the right side: 0.067193392

Break this problem into two subproblems by setting 
(x + -0.1613207547) equal to 0.067193392 and -0.067193392.

Subproblem 1

x + -0.1613207547 = 0.067193392 Simplifying x + -0.1613207547 = 0.067193392 Reorder the terms: -0.1613207547 + x = 0.067193392 Solving -0.1613207547 + x = 0.067193392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1613207547' to each side of the equation. -0.1613207547 + 0.1613207547 + x = 0.067193392 + 0.1613207547 Combine like terms: -0.1613207547 + 0.1613207547 = 0.0000000000 0.0000000000 + x = 0.067193392 + 0.1613207547 x = 0.067193392 + 0.1613207547 Combine like terms: 0.067193392 + 0.1613207547 = 0.2285141467 x = 0.2285141467 Simplifying x = 0.2285141467

Subproblem 2

x + -0.1613207547 = -0.067193392 Simplifying x + -0.1613207547 = -0.067193392 Reorder the terms: -0.1613207547 + x = -0.067193392 Solving -0.1613207547 + x = -0.067193392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1613207547' to each side of the equation. -0.1613207547 + 0.1613207547 + x = -0.067193392 + 0.1613207547 Combine like terms: -0.1613207547 + 0.1613207547 = 0.0000000000 0.0000000000 + x = -0.067193392 + 0.1613207547 x = -0.067193392 + 0.1613207547 Combine like terms: -0.067193392 + 0.1613207547 = 0.0941273627 x = 0.0941273627 Simplifying x = 0.0941273627

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2285141467, 0.0941273627}

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