(x-4)+(x-5)(x+5)=2(x+2)+24

Simple and best practice solution for (x-4)+(x-5)(x+5)=2(x+2)+24 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 (x-4)+(x-5)(x+5)=2(x+2)+24 equation:


Simplifying
(x + -4) + (x + -5)(x + 5) = 2(x + 2) + 24

Reorder the terms:
(-4 + x) + (x + -5)(x + 5) = 2(x + 2) + 24

Remove parenthesis around (-4 + x)
-4 + x + (x + -5)(x + 5) = 2(x + 2) + 24

Reorder the terms:
-4 + x + (-5 + x)(x + 5) = 2(x + 2) + 24

Reorder the terms:
-4 + x + (-5 + x)(5 + x) = 2(x + 2) + 24

Multiply (-5 + x) * (5 + x)
-4 + x + (-5(5 + x) + x(5 + x)) = 2(x + 2) + 24
-4 + x + ((5 * -5 + x * -5) + x(5 + x)) = 2(x + 2) + 24
-4 + x + ((-25 + -5x) + x(5 + x)) = 2(x + 2) + 24
-4 + x + (-25 + -5x + (5 * x + x * x)) = 2(x + 2) + 24
-4 + x + (-25 + -5x + (5x + x2)) = 2(x + 2) + 24

Combine like terms: -5x + 5x = 0
-4 + x + (-25 + 0 + x2) = 2(x + 2) + 24
-4 + x + (-25 + x2) = 2(x + 2) + 24

Reorder the terms:
-4 + -25 + x + x2 = 2(x + 2) + 24

Combine like terms: -4 + -25 = -29
-29 + x + x2 = 2(x + 2) + 24

Reorder the terms:
-29 + x + x2 = 2(2 + x) + 24
-29 + x + x2 = (2 * 2 + x * 2) + 24
-29 + x + x2 = (4 + 2x) + 24

Reorder the terms:
-29 + x + x2 = 4 + 24 + 2x

Combine like terms: 4 + 24 = 28
-29 + x + x2 = 28 + 2x

Solving
-29 + x + x2 = 28 + 2x

Solving for variable 'x'.

Reorder the terms:
-29 + -28 + x + -2x + x2 = 28 + 2x + -28 + -2x

Combine like terms: -29 + -28 = -57
-57 + x + -2x + x2 = 28 + 2x + -28 + -2x

Combine like terms: x + -2x = -1x
-57 + -1x + x2 = 28 + 2x + -28 + -2x

Reorder the terms:
-57 + -1x + x2 = 28 + -28 + 2x + -2x

Combine like terms: 28 + -28 = 0
-57 + -1x + x2 = 0 + 2x + -2x
-57 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-57 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + -1x + 57 + x2 = 0 + 57

Reorder the terms:
-57 + 57 + -1x + x2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + -1x + x2 = 0 + 57
-1x + x2 = 0 + 57

Combine like terms: 0 + 57 = 57
-1x + x2 = 57

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 57 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 57 + 0.25

Combine like terms: 57 + 0.25 = 57.25
0.25 + -1x + x2 = 57.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(x + -0.5) equal to 7.566372975 and -7.566372975.

Subproblem 1

x + -0.5 = 7.566372975 Simplifying x + -0.5 = 7.566372975 Reorder the terms: -0.5 + x = 7.566372975 Solving -0.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 7.566372975 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.566372975 + 0.5 x = 7.566372975 + 0.5 Combine like terms: 7.566372975 + 0.5 = 8.066372975 x = 8.066372975 Simplifying x = 8.066372975

Subproblem 2

x + -0.5 = -7.566372975 Simplifying x + -0.5 = -7.566372975 Reorder the terms: -0.5 + x = -7.566372975 Solving -0.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -7.566372975 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.566372975 + 0.5 x = -7.566372975 + 0.5 Combine like terms: -7.566372975 + 0.5 = -7.066372975 x = -7.066372975 Simplifying x = -7.066372975

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.066372975, -7.066372975}

See similar equations:

| 2a+5/9=-3 | | -12x-13=4x+3 | | h=16t^2+441 | | -4x-3x-3x-3= | | 2a+5/9=-7 | | y=16x^2+441 | | h=16x^2+441 | | 3/2(-2)-1/3y=4 | | 40x+70=118.40 | | x+39=-16 | | y/8+5=9/2 | | 4(4)+x=5(2x-4) | | 16(a-5)=-8 | | x+63+x+63=x+125 | | -8x+9=49 | | 9b+6=21 | | x/14=5/7 | | 6(6v-5)=-138 | | y=3x^2+14x-49 | | 6t-36+6t=12t+12 | | 9a+7-4a=-3 | | 1-1/3*39=14 | | d^2+7d=10 | | 2/5x+8=4-1/10x | | f(x)=2x-4 | | 10-(-16)= | | 4(4)+x=5(2x-y) | | 12x+24=12x+36-12 | | 201=24-w | | 2n(n+4)+(n-2)-15=3n(-n+1)+2n+6 | | 1.2y+3=0.36(-2) | | -13=5y+2 |

Equations solver categories