x^2+1.5x+0.5625=3

Simple and best practice solution for x^2+1.5x+0.5625=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+1.5x+0.5625=3 equation: 


Simplifying
x2 + 1.5x + 0.5625 = 3

Reorder the terms:
0.5625 + 1.5x + x2 = 3

Solving
0.5625 + 1.5x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
0.5625 + -3 + 1.5x + x2 = 3 + -3

Combine like terms: 0.5625 + -3 = -2.4375
-2.4375 + 1.5x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-2.4375 + 1.5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2.4375' to each side of the equation.
-2.4375 + 1.5x + 2.4375 + x2 = 0 + 2.4375

Reorder the terms:
-2.4375 + 2.4375 + 1.5x + x2 = 0 + 2.4375

Combine like terms: -2.4375 + 2.4375 = 0.0000
0.0000 + 1.5x + x2 = 0 + 2.4375
1.5x + x2 = 0 + 2.4375

Combine like terms: 0 + 2.4375 = 2.4375
1.5x + x2 = 2.4375

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 2.4375 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 2.4375 + 0.5625

Combine like terms: 2.4375 + 0.5625 = 3
0.5625 + 1.5x + x2 = 3

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + 0.75 = 1.732050808

Simplifying
x + 0.75 = 1.732050808

Reorder the terms:
0.75 + x = 1.732050808

Solving
0.75 + x = 1.732050808

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 1.732050808 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.732050808 + -0.75
x = 1.732050808 + -0.75

Combine like terms: 1.732050808 + -0.75 = 0.982050808
x = 0.982050808

Simplifying
x = 0.982050808


Subproblem 2
x + 0.75 = -1.732050808

Simplifying
x + 0.75 = -1.732050808

Reorder the terms:
0.75 + x = -1.732050808

Solving
0.75 + x = -1.732050808

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -1.732050808 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.732050808 + -0.75
x = -1.732050808 + -0.75

Combine like terms: -1.732050808 + -0.75 = -2.482050808
x = -2.482050808

Simplifying
x = -2.482050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.982050808, -2.482050808}

See similar equations:

| 5-2(x-2)=12 | | -.5(4x-2)=11 | | 20x+16y+510x-6y-5= | | 5b+7a+15-a+2b=10 | | -63+w=55 | | 5x-(x-10)=-6 | | 3x=9x-12 | | -(3x-10)=12 | | x^2-12x-108=0 | | X=4x+2x+3x+2 | | -2(x-.5)=-2 | | .5x+.25=3.75 | | x^2-9x+20.25=0 | | 3x+10+2x-14+x-2=180 | | 63=9(2-a) | | 4x+5(7x-3)=9(16-3d) | | 3v^2+7v=-4 | | 2[2(x+y)-4(4x-5y)]= | | 7b-4=2b+16 | | 7b-4=2b+16 | | 3v^2+7=-4 | | 15=-3(c-1)+a | | 40-5n=-2 | | 5m+2m(m+1)=23 | | y=8-3 | | y=5*7+1 | | (8x+y+1)(3x)= | | y=-2*-5+2 | | 8-4x=-8x+16 | | y=-3*-6+6 | | 4(x-2)=2(x+3) | | y=4*6+4 |

Equations solver categories