4x+3.14(x)(x)=1300

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Solution for 4x+3.14(x)(x)=1300 equation:


Simplifying
4x + 3.14(x)(x) = 1300

Multiply x * x
4x + 3.14x2 = 1300

Solving
4x + 3.14x2 = 1300

Solving for variable 'x'.

Reorder the terms:
-1300 + 4x + 3.14x2 = 1300 + -1300

Combine like terms: 1300 + -1300 = 0
-1300 + 4x + 3.14x2 = 0

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

Divide each side by '3.14'.
-414.0127389 + 1.27388535x + x2 = 0

Move the constant term to the right:

Add '414.0127389' to each side of the equation.
-414.0127389 + 1.27388535x + 414.0127389 + x2 = 0 + 414.0127389

Reorder the terms:
-414.0127389 + 414.0127389 + 1.27388535x + x2 = 0 + 414.0127389

Combine like terms: -414.0127389 + 414.0127389 = 0.0000000
0.0000000 + 1.27388535x + x2 = 0 + 414.0127389
1.27388535x + x2 = 0 + 414.0127389

Combine like terms: 0 + 414.0127389 = 414.0127389
1.27388535x + x2 = 414.0127389

The x term is 1.27388535x.  Take half its coefficient (0.636942675).
Square it (0.4056959712) and add it to both sides.

Add '0.4056959712' to each side of the equation.
1.27388535x + 0.4056959712 + x2 = 414.0127389 + 0.4056959712

Reorder the terms:
0.4056959712 + 1.27388535x + x2 = 414.0127389 + 0.4056959712

Combine like terms: 414.0127389 + 0.4056959712 = 414.4184348712
0.4056959712 + 1.27388535x + x2 = 414.4184348712

Factor a perfect square on the left side:
(x + 0.636942675)(x + 0.636942675) = 414.4184348712

Calculate the square root of the right side: 20.357269829

Break this problem into two subproblems by setting 
(x + 0.636942675) equal to 20.357269829 and -20.357269829.

Subproblem 1

x + 0.636942675 = 20.357269829 Simplifying x + 0.636942675 = 20.357269829 Reorder the terms: 0.636942675 + x = 20.357269829 Solving 0.636942675 + x = 20.357269829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.636942675' to each side of the equation. 0.636942675 + -0.636942675 + x = 20.357269829 + -0.636942675 Combine like terms: 0.636942675 + -0.636942675 = 0.000000000 0.000000000 + x = 20.357269829 + -0.636942675 x = 20.357269829 + -0.636942675 Combine like terms: 20.357269829 + -0.636942675 = 19.720327154 x = 19.720327154 Simplifying x = 19.720327154

Subproblem 2

x + 0.636942675 = -20.357269829 Simplifying x + 0.636942675 = -20.357269829 Reorder the terms: 0.636942675 + x = -20.357269829 Solving 0.636942675 + x = -20.357269829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.636942675' to each side of the equation. 0.636942675 + -0.636942675 + x = -20.357269829 + -0.636942675 Combine like terms: 0.636942675 + -0.636942675 = 0.000000000 0.000000000 + x = -20.357269829 + -0.636942675 x = -20.357269829 + -0.636942675 Combine like terms: -20.357269829 + -0.636942675 = -20.994212504 x = -20.994212504 Simplifying x = -20.994212504

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.720327154, -20.994212504}

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