5x^2=x+10

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Solution for 5x^2=x+10 equation:


Simplifying
5x2 = x + 10

Reorder the terms:
5x2 = 10 + x

Solving
5x2 = 10 + x

Solving for variable 'x'.

Reorder the terms:
-10 + -1x + 5x2 = 10 + x + -10 + -1x

Reorder the terms:
-10 + -1x + 5x2 = 10 + -10 + x + -1x

Combine like terms: 10 + -10 = 0
-10 + -1x + 5x2 = 0 + x + -1x
-10 + -1x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-10 + -1x + 5x2 = 0

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

Divide each side by '5'.
-2 + -0.2x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.2x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.2x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.2x + x2 = 0 + 2
-0.2x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.2x + x2 = 2

The x term is -0.2x.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2x + 0.01 + x2 = 2 + 0.01

Reorder the terms:
0.01 + -0.2x + x2 = 2 + 0.01

Combine like terms: 2 + 0.01 = 2.01
0.01 + -0.2x + x2 = 2.01

Factor a perfect square on the left side:
(x + -0.1)(x + -0.1) = 2.01

Calculate the square root of the right side: 1.417744688

Break this problem into two subproblems by setting 
(x + -0.1) equal to 1.417744688 and -1.417744688.

Subproblem 1

x + -0.1 = 1.417744688 Simplifying x + -0.1 = 1.417744688 Reorder the terms: -0.1 + x = 1.417744688 Solving -0.1 + x = 1.417744688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.417744688 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.417744688 + 0.1 x = 1.417744688 + 0.1 Combine like terms: 1.417744688 + 0.1 = 1.517744688 x = 1.517744688 Simplifying x = 1.517744688

Subproblem 2

x + -0.1 = -1.417744688 Simplifying x + -0.1 = -1.417744688 Reorder the terms: -0.1 + x = -1.417744688 Solving -0.1 + x = -1.417744688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.417744688 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.417744688 + 0.1 x = -1.417744688 + 0.1 Combine like terms: -1.417744688 + 0.1 = -1.317744688 x = -1.317744688 Simplifying x = -1.317744688

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.517744688, -1.317744688}

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