5x^2-2x=470

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Solution for 5x^2-2x=470 equation:


Simplifying
5x2 + -2x = 470

Reorder the terms:
-2x + 5x2 = 470

Solving
-2x + 5x2 = 470

Solving for variable 'x'.

Reorder the terms:
-470 + -2x + 5x2 = 470 + -470

Combine like terms: 470 + -470 = 0
-470 + -2x + 5x2 = 0

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

Divide each side by '5'.
-94 + -0.4x + x2 = 0

Move the constant term to the right:

Add '94' to each side of the equation.
-94 + -0.4x + 94 + x2 = 0 + 94

Reorder the terms:
-94 + 94 + -0.4x + x2 = 0 + 94

Combine like terms: -94 + 94 = 0
0 + -0.4x + x2 = 0 + 94
-0.4x + x2 = 0 + 94

Combine like terms: 0 + 94 = 94
-0.4x + x2 = 94

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 94 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 94 + 0.04

Combine like terms: 94 + 0.04 = 94.04
0.04 + -0.4x + x2 = 94.04

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 94.04

Calculate the square root of the right side: 9.697422338

Break this problem into two subproblems by setting 
(x + -0.2) equal to 9.697422338 and -9.697422338.

Subproblem 1

x + -0.2 = 9.697422338 Simplifying x + -0.2 = 9.697422338 Reorder the terms: -0.2 + x = 9.697422338 Solving -0.2 + x = 9.697422338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 9.697422338 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 9.697422338 + 0.2 x = 9.697422338 + 0.2 Combine like terms: 9.697422338 + 0.2 = 9.897422338 x = 9.897422338 Simplifying x = 9.897422338

Subproblem 2

x + -0.2 = -9.697422338 Simplifying x + -0.2 = -9.697422338 Reorder the terms: -0.2 + x = -9.697422338 Solving -0.2 + x = -9.697422338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -9.697422338 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -9.697422338 + 0.2 x = -9.697422338 + 0.2 Combine like terms: -9.697422338 + 0.2 = -9.497422338 x = -9.497422338 Simplifying x = -9.497422338

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.897422338, -9.497422338}

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