3.14x^2-x-36(3.14)=0

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Solution for 3.14x^2-x-36(3.14)=0 equation:


Simplifying
3.14x2 + -1x + -36(3.14) = 0

Multiply -36 * 3.14
3.14x2 + -1x + -113.04 = 0

Reorder the terms:
-113.04 + -1x + 3.14x2 = 0

Solving
-113.04 + -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'.
-36 + -0.3184713376x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -0.3184713376x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -0.3184713376x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -0.3184713376x + x2 = 0 + 36
-0.3184713376x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-0.3184713376x + x2 = 36

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 = 36 + 0.02535599822

Reorder the terms:
0.02535599822 + -0.3184713376x + x2 = 36 + 0.02535599822

Combine like terms: 36 + 0.02535599822 = 36.02535599822
0.02535599822 + -0.3184713376x + x2 = 36.02535599822

Factor a perfect square on the left side:
(x + -0.1592356688)(x + -0.1592356688) = 36.02535599822

Calculate the square root of the right side: 6.002112628

Break this problem into two subproblems by setting 
(x + -0.1592356688) equal to 6.002112628 and -6.002112628.

Subproblem 1

x + -0.1592356688 = 6.002112628 Simplifying x + -0.1592356688 = 6.002112628 Reorder the terms: -0.1592356688 + x = 6.002112628 Solving -0.1592356688 + x = 6.002112628 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 = 6.002112628 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = 6.002112628 + 0.1592356688 x = 6.002112628 + 0.1592356688 Combine like terms: 6.002112628 + 0.1592356688 = 6.1613482968 x = 6.1613482968 Simplifying x = 6.1613482968

Subproblem 2

x + -0.1592356688 = -6.002112628 Simplifying x + -0.1592356688 = -6.002112628 Reorder the terms: -0.1592356688 + x = -6.002112628 Solving -0.1592356688 + x = -6.002112628 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 = -6.002112628 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = -6.002112628 + 0.1592356688 x = -6.002112628 + 0.1592356688 Combine like terms: -6.002112628 + 0.1592356688 = -5.8428769592 x = -5.8428769592 Simplifying x = -5.8428769592

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.1613482968, -5.8428769592}

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