x^2+1.414213562x=3

Simple and best practice solution for x^2+1.414213562x=3 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+1.414213562x=3 equation:


Simplifying
x2 + 1.414213562x = 3

Reorder the terms:
1.414213562x + x2 = 3

Solving
1.414213562x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 1.414213562x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 1.414213562x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1.414213562x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 1.414213562x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1.414213562x + x2 = 0 + 3
1.414213562x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
1.414213562x + x2 = 3

The x term is 1.414213562x.  Take half its coefficient (0.707106781).
Square it (0.4999999997) and add it to both sides.

Add '0.4999999997' to each side of the equation.
1.414213562x + 0.4999999997 + x2 = 3 + 0.4999999997

Reorder the terms:
0.4999999997 + 1.414213562x + x2 = 3 + 0.4999999997

Combine like terms: 3 + 0.4999999997 = 3.4999999997
0.4999999997 + 1.414213562x + x2 = 3.4999999997

Factor a perfect square on the left side:
(x + 0.707106781)(x + 0.707106781) = 3.4999999997

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(x + 0.707106781) equal to 1.870828693 and -1.870828693.

Subproblem 1

x + 0.707106781 = 1.870828693 Simplifying x + 0.707106781 = 1.870828693 Reorder the terms: 0.707106781 + x = 1.870828693 Solving 0.707106781 + x = 1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.707106781' to each side of the equation. 0.707106781 + -0.707106781 + x = 1.870828693 + -0.707106781 Combine like terms: 0.707106781 + -0.707106781 = 0.000000000 0.000000000 + x = 1.870828693 + -0.707106781 x = 1.870828693 + -0.707106781 Combine like terms: 1.870828693 + -0.707106781 = 1.163721912 x = 1.163721912 Simplifying x = 1.163721912

Subproblem 2

x + 0.707106781 = -1.870828693 Simplifying x + 0.707106781 = -1.870828693 Reorder the terms: 0.707106781 + x = -1.870828693 Solving 0.707106781 + x = -1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.707106781' to each side of the equation. 0.707106781 + -0.707106781 + x = -1.870828693 + -0.707106781 Combine like terms: 0.707106781 + -0.707106781 = 0.000000000 0.000000000 + x = -1.870828693 + -0.707106781 x = -1.870828693 + -0.707106781 Combine like terms: -1.870828693 + -0.707106781 = -2.577935474 x = -2.577935474 Simplifying x = -2.577935474

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.163721912, -2.577935474}

See similar equations:

| 6x-15=8x+23 | | 10-d=-34-54 | | (6x^3)-(7x^2)+(20x)+25=0 | | 8-y=8-6 | | -(z-6)=0.5(4z-8) | | 8d-3d=66 | | -12=2+5w+2w | | x(1.2-2x)(0.8-2x)= | | 3(w-4)+w=2w+14 | | 1/3(x)-3=-2 | | f=5+3x-1+9x | | 2x^2-7x+8=5 | | 8+2(2-x)=3(x-2) | | 4[6x-1]=29 | | 4.87=-.15+4.9 | | 56-10n-n^2=0 | | x^2+4.6x=319 | | x^2+6.9x=128 | | X=-.15t+4.9 | | 3(2y+3)=6Y+9 | | 4a^4+2a^3+8a= | | 7x^2-18=38 | | 5[x+4]=45 | | 16-(x+4)=2(1-x)+4 | | 4+3x=-10 | | 3(2+2x)=6x+3 | | 0.5(10x+10)=6x-8 | | 9(3x)(x)-5x=3(x)(9x)+11 | | 10*sin^2x+3*cosx-9=0 | | 0=3x^2+3x+0 | | (x-2)*(x+5)=0 | | x^2+5x=85.25 |

Equations solver categories