(2-3x)2+(1+4x)2=(5x-1)(5x-1)

Simple and best practice solution for (2-3x)2+(1+4x)2=(5x-1)(5x-1) 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 (2-3x)2+(1+4x)2=(5x-1)(5x-1) equation:


Simplifying
(2 + -3x) * 2 + (1 + 4x) * 2 = (5x + -1)(5x + -1)

Reorder the terms for easier multiplication:
2(2 + -3x) + (1 + 4x) * 2 = (5x + -1)(5x + -1)
(2 * 2 + -3x * 2) + (1 + 4x) * 2 = (5x + -1)(5x + -1)
(4 + -6x) + (1 + 4x) * 2 = (5x + -1)(5x + -1)

Reorder the terms for easier multiplication:
4 + -6x + 2(1 + 4x) = (5x + -1)(5x + -1)
4 + -6x + (1 * 2 + 4x * 2) = (5x + -1)(5x + -1)
4 + -6x + (2 + 8x) = (5x + -1)(5x + -1)

Reorder the terms:
4 + 2 + -6x + 8x = (5x + -1)(5x + -1)

Combine like terms: 4 + 2 = 6
6 + -6x + 8x = (5x + -1)(5x + -1)

Combine like terms: -6x + 8x = 2x
6 + 2x = (5x + -1)(5x + -1)

Reorder the terms:
6 + 2x = (-1 + 5x)(5x + -1)

Reorder the terms:
6 + 2x = (-1 + 5x)(-1 + 5x)

Multiply (-1 + 5x) * (-1 + 5x)
6 + 2x = (-1(-1 + 5x) + 5x * (-1 + 5x))
6 + 2x = ((-1 * -1 + 5x * -1) + 5x * (-1 + 5x))
6 + 2x = ((1 + -5x) + 5x * (-1 + 5x))
6 + 2x = (1 + -5x + (-1 * 5x + 5x * 5x))
6 + 2x = (1 + -5x + (-5x + 25x2))

Combine like terms: -5x + -5x = -10x
6 + 2x = (1 + -10x + 25x2)

Solving
6 + 2x = 1 + -10x + 25x2

Solving for variable 'x'.

Reorder the terms:
6 + -1 + 2x + 10x + -25x2 = 1 + -10x + 25x2 + -1 + 10x + -25x2

Combine like terms: 6 + -1 = 5
5 + 2x + 10x + -25x2 = 1 + -10x + 25x2 + -1 + 10x + -25x2

Combine like terms: 2x + 10x = 12x
5 + 12x + -25x2 = 1 + -10x + 25x2 + -1 + 10x + -25x2

Reorder the terms:
5 + 12x + -25x2 = 1 + -1 + -10x + 10x + 25x2 + -25x2

Combine like terms: 1 + -1 = 0
5 + 12x + -25x2 = 0 + -10x + 10x + 25x2 + -25x2
5 + 12x + -25x2 = -10x + 10x + 25x2 + -25x2

Combine like terms: -10x + 10x = 0
5 + 12x + -25x2 = 0 + 25x2 + -25x2
5 + 12x + -25x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
5 + 12x + -25x2 = 0

Begin completing the square.  Divide all terms by
-25 the coefficient of the squared term: 

Divide each side by '-25'.
-0.2 + -0.48x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.48x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.48x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.48x + x2 = 0 + 0.2
-0.48x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.48x + x2 = 0.2

The x term is -0.48x.  Take half its coefficient (-0.24).
Square it (0.0576) and add it to both sides.

Add '0.0576' to each side of the equation.
-0.48x + 0.0576 + x2 = 0.2 + 0.0576

Reorder the terms:
0.0576 + -0.48x + x2 = 0.2 + 0.0576

Combine like terms: 0.2 + 0.0576 = 0.2576
0.0576 + -0.48x + x2 = 0.2576

Factor a perfect square on the left side:
(x + -0.24)(x + -0.24) = 0.2576

Calculate the square root of the right side: 0.507543102

Break this problem into two subproblems by setting 
(x + -0.24) equal to 0.507543102 and -0.507543102.

Subproblem 1

x + -0.24 = 0.507543102 Simplifying x + -0.24 = 0.507543102 Reorder the terms: -0.24 + x = 0.507543102 Solving -0.24 + x = 0.507543102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.24' to each side of the equation. -0.24 + 0.24 + x = 0.507543102 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + x = 0.507543102 + 0.24 x = 0.507543102 + 0.24 Combine like terms: 0.507543102 + 0.24 = 0.747543102 x = 0.747543102 Simplifying x = 0.747543102

Subproblem 2

x + -0.24 = -0.507543102 Simplifying x + -0.24 = -0.507543102 Reorder the terms: -0.24 + x = -0.507543102 Solving -0.24 + x = -0.507543102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.24' to each side of the equation. -0.24 + 0.24 + x = -0.507543102 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + x = -0.507543102 + 0.24 x = -0.507543102 + 0.24 Combine like terms: -0.507543102 + 0.24 = -0.267543102 x = -0.267543102 Simplifying x = -0.267543102

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.747543102, -0.267543102}

See similar equations:

| -2.5p=+500p | | 0.6h=36 | | 0,85(x-3)=x-15 | | 2(3x+12)=2(4x+8) | | 4x-5=14x-115 | | -15+x=x+16 | | 4y+5=13 | | 4y+5=13whatisY | | 6y^2+8y+5=0 | | 3x+2-(4x+5)= | | -4(8-x)+15=-51 | | y=4x^2+9x-2 | | 3x+3x+5=11x | | 2a+b=1 | | 13x+y=11 | | -42-7x=8x+18 | | 2c+3/12=1/4 | | 5x+2+3x=-6 | | 2x+6=8y | | 6m-3/7=9 | | ax+9=3x+b | | 4x=4y+12 | | a/4-3=9 | | 1x+1x=4 | | 4.8=2.4y | | 6y-10=4y | | -12x-20=10x+50 | | 3x^2-43x+74=0 | | 2x^2-5x= | | 0.2t=3 | | 4x^2-4x-38=0 | | Y^2+20y-144=0 |

Equations solver categories