3.14x^2-x-(54*3.14)=0

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Solution for 3.14x^2-x-(54*3.14)=0 equation:


Simplifying
3.14x2 + -1x + -1(54 * 3.14) = 0

Multiply 54 * 3.14
3.14x2 + -1x + -1(169.56) = 0

Multiply -1 * 169.56
3.14x2 + -1x + -169.56 = 0

Reorder the terms:
-169.56 + -1x + 3.14x2 = 0

Solving
-169.56 + -1x + 3.14x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.14'.
-54 + -0.3184713376x + x2 = 0

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -0.3184713376x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -0.3184713376x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -0.3184713376x + x2 = 0 + 54
-0.3184713376x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-0.3184713376x + x2 = 54

The x term is -0.3184713376x.  Take half its coefficient (-0.1592356688).
Square it (0.02535599822) and add it to both sides.

Add '0.02535599822' to each side of the equation.
-0.3184713376x + 0.02535599822 + x2 = 54 + 0.02535599822

Reorder the terms:
0.02535599822 + -0.3184713376x + x2 = 54 + 0.02535599822

Combine like terms: 54 + 0.02535599822 = 54.02535599822
0.02535599822 + -0.3184713376x + x2 = 54.02535599822

Factor a perfect square on the left side:
(x + -0.1592356688)(x + -0.1592356688) = 54.02535599822

Calculate the square root of the right side: 7.350194283

Break this problem into two subproblems by setting 
(x + -0.1592356688) equal to 7.350194283 and -7.350194283.

Subproblem 1

x + -0.1592356688 = 7.350194283 Simplifying x + -0.1592356688 = 7.350194283 Reorder the terms: -0.1592356688 + x = 7.350194283 Solving -0.1592356688 + x = 7.350194283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1592356688' to each side of the equation. -0.1592356688 + 0.1592356688 + x = 7.350194283 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = 7.350194283 + 0.1592356688 x = 7.350194283 + 0.1592356688 Combine like terms: 7.350194283 + 0.1592356688 = 7.5094299518 x = 7.5094299518 Simplifying x = 7.5094299518

Subproblem 2

x + -0.1592356688 = -7.350194283 Simplifying x + -0.1592356688 = -7.350194283 Reorder the terms: -0.1592356688 + x = -7.350194283 Solving -0.1592356688 + x = -7.350194283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1592356688' to each side of the equation. -0.1592356688 + 0.1592356688 + x = -7.350194283 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = -7.350194283 + 0.1592356688 x = -7.350194283 + 0.1592356688 Combine like terms: -7.350194283 + 0.1592356688 = -7.1909586142 x = -7.1909586142 Simplifying x = -7.1909586142

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.5094299518, -7.1909586142}

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