((0.3-x)(0.3-x))=0.2x(0.2+x)

Simple and best practice solution for ((0.3-x)(0.3-x))=0.2x(0.2+x) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for ((0.3-x)(0.3-x))=0.2x(0.2+x) equation:


Simplifying
((0.3 + -1x)(0.3 + -1x)) = 0.2x(0.2 + x)

Multiply (0.3 + -1x) * (0.3 + -1x)
((0.3(0.3 + -1x) + -1x * (0.3 + -1x))) = 0.2x(0.2 + x)
(((0.3 * 0.3 + -1x * 0.3) + -1x * (0.3 + -1x))) = 0.2x(0.2 + x)
(((0.09 + -0.3x) + -1x * (0.3 + -1x))) = 0.2x(0.2 + x)
((0.09 + -0.3x + (0.3 * -1x + -1x * -1x))) = 0.2x(0.2 + x)
((0.09 + -0.3x + (-0.3x + 1x2))) = 0.2x(0.2 + x)

Combine like terms: -0.3x + -0.3x = -0.6x
((0.09 + -0.6x + 1x2)) = 0.2x(0.2 + x)
(0.09 + -0.6x + 1x2) = 0.2x(0.2 + x)

Remove parenthesis around (0.09 + -0.6x + 1x2)
0.09 + -0.6x + 1x2 = 0.2x(0.2 + x)
0.09 + -0.6x + 1x2 = (0.2 * 0.2x + x * 0.2x)
0.09 + -0.6x + 1x2 = (0.04x + 0.2x2)

Solving
0.09 + -0.6x + 1x2 = 0.04x + 0.2x2

Solving for variable 'x'.

Reorder the terms:
0.09 + -0.6x + -0.04x + 1x2 + -0.2x2 = 0.04x + 0.2x2 + -0.04x + -0.2x2

Combine like terms: -0.6x + -0.04x = -0.64x
0.09 + -0.64x + 1x2 + -0.2x2 = 0.04x + 0.2x2 + -0.04x + -0.2x2

Combine like terms: 1x2 + -0.2x2 = 0.8x2
0.09 + -0.64x + 0.8x2 = 0.04x + 0.2x2 + -0.04x + -0.2x2

Reorder the terms:
0.09 + -0.64x + 0.8x2 = 0.04x + -0.04x + 0.2x2 + -0.2x2

Combine like terms: 0.04x + -0.04x = 0.00
0.09 + -0.64x + 0.8x2 = 0.00 + 0.2x2 + -0.2x2
0.09 + -0.64x + 0.8x2 = 0.2x2 + -0.2x2

Combine like terms: 0.2x2 + -0.2x2 = 0.0
0.09 + -0.64x + 0.8x2 = 0.0

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

Divide each side by '0.8'.
0.1125 + -0.8x + x2 = 0

Move the constant term to the right:

Add '-0.1125' to each side of the equation.
0.1125 + -0.8x + -0.1125 + x2 = 0 + -0.1125

Reorder the terms:
0.1125 + -0.1125 + -0.8x + x2 = 0 + -0.1125

Combine like terms: 0.1125 + -0.1125 = 0.0000
0.0000 + -0.8x + x2 = 0 + -0.1125
-0.8x + x2 = 0 + -0.1125

Combine like terms: 0 + -0.1125 = -0.1125
-0.8x + x2 = -0.1125

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = -0.1125 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = -0.1125 + 0.16

Combine like terms: -0.1125 + 0.16 = 0.0475
0.16 + -0.8x + x2 = 0.0475

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.0475

Calculate the square root of the right side: 0.217944947

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.217944947 and -0.217944947.

Subproblem 1

x + -0.4 = 0.217944947 Simplifying x + -0.4 = 0.217944947 Reorder the terms: -0.4 + x = 0.217944947 Solving -0.4 + x = 0.217944947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.217944947 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.217944947 + 0.4 x = 0.217944947 + 0.4 Combine like terms: 0.217944947 + 0.4 = 0.617944947 x = 0.617944947 Simplifying x = 0.617944947

Subproblem 2

x + -0.4 = -0.217944947 Simplifying x + -0.4 = -0.217944947 Reorder the terms: -0.4 + x = -0.217944947 Solving -0.4 + x = -0.217944947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.217944947 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.217944947 + 0.4 x = -0.217944947 + 0.4 Combine like terms: -0.217944947 + 0.4 = 0.182055053 x = 0.182055053 Simplifying x = 0.182055053

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.617944947, 0.182055053}

See similar equations:

| x^2+24x+x=0 | | 4x-2=5x-20 | | 1/5(x-4)^2=15 | | 1/4(3x)=12 | | 4x^2=3000 | | x^2+20x-27=0 | | (2x-5)-(3x-7)= | | 3(y-3)=9y+3-2(-6y-2) | | 2x+12=3+6x-7 | | 2(x-(4+2x)+3)=2x+7 | | 2(y-3)-6=-4(-5y+2)-4y | | 8x-2x+60=8x+38 | | -2(3w-1)+4w=4+3(4w-4) | | n=725+2.75n | | (8x-4)-(x-2)= | | 7-9x-3=-16+7x-12 | | 4v-4+4(2v+2)=-2(v+2) | | 7x+9x-60=100-4x | | -8x-13=7x+17 | | x^2+y^2+z^2-16z=0 | | (X-2)(x-7)+14=0 | | (5x-5)-(2x+2)= | | 25-4x=6x | | 2x-4(x-2)=-9+4x-13 | | -x/4-8=9 | | 6x-9y-3y+8x+4= | | (8x-3)-(2x-5)= | | -x-9=-7x+21 | | 11+3p=(-7p-6) | | -4(5t-5)+6t=4t-3 | | 14*333.3333+10y=4000 | | -7i(-3+i)(2-4i)-(6-4i)=0 |

Equations solver categories