x^2+1=-5x

Simple and best practice solution for x^2+1=-5x 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^2+1=-5x equation:


Simplifying
x2 + 1 = -5x

Reorder the terms:
1 + x2 = -5x

Solving
1 + x2 = -5x

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 5x + x2 = 0 + -1

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

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

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -1 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -1 + 6.25

Combine like terms: -1 + 6.25 = 5.25
6.25 + 5x + x2 = 5.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + 2.5 = 2.291287847 Simplifying x + 2.5 = 2.291287847 Reorder the terms: 2.5 + x = 2.291287847 Solving 2.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.291287847 + -2.5 x = 2.291287847 + -2.5 Combine like terms: 2.291287847 + -2.5 = -0.208712153 x = -0.208712153 Simplifying x = -0.208712153

Subproblem 2

x + 2.5 = -2.291287847 Simplifying x + 2.5 = -2.291287847 Reorder the terms: 2.5 + x = -2.291287847 Solving 2.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.291287847 + -2.5 x = -2.291287847 + -2.5 Combine like terms: -2.291287847 + -2.5 = -4.791287847 x = -4.791287847 Simplifying x = -4.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.208712153, -4.791287847}

See similar equations:

| -3z+8z=-z-6-5z | | (3x+8)+(-4x+1)= | | -2(2s-5)-10=-3(6s+1)-3 | | X^2-15x=18 | | 3tan^3(x)=tan(x) | | s^4-r^4=0 | | 4/p=5/8 | | 9/6=3 | | (X/5)-3=-7 | | 0=-3x-4+4y | | Y-2/7=6/7 | | -2(3x-2)+12=4 | | -2(2s-5)-10=-3(8s+1)-3 | | 3x*x*y=1410 | | 2(b+8)= | | 1/2x5= | | -16t^2+40t+6=3 | | -(t-5g+4a)= | | 160=52-u | | (3+5)2-13= | | 25.12=1/3(12.56h | | Y/-4=12 | | 5x^2+(-1)(-4)+4= | | .10x+.05(6-x)=.10(11) | | 1.68=d*2 | | 42-12n*2=n | | 5(2-u)-u=2(u-1) | | 5.25x-6.12=2.78x+9.88 | | .14x=x+18000 | | 31=3x-17 | | 15=1/2b(3) | | 7-3x(-6)-9= |

Equations solver categories