2x-3=x^2+3x-7

Simple and best practice solution for 2x-3=x^2+3x-7 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 2x-3=x^2+3x-7 equation:


Simplifying
2x + -3 = x2 + 3x + -7

Reorder the terms:
-3 + 2x = x2 + 3x + -7

Reorder the terms:
-3 + 2x = -7 + 3x + x2

Solving
-3 + 2x = -7 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + 7 + 2x + -3x + -1x2 = -7 + 3x + x2 + 7 + -3x + -1x2

Combine like terms: -3 + 7 = 4
4 + 2x + -3x + -1x2 = -7 + 3x + x2 + 7 + -3x + -1x2

Combine like terms: 2x + -3x = -1x
4 + -1x + -1x2 = -7 + 3x + x2 + 7 + -3x + -1x2

Reorder the terms:
4 + -1x + -1x2 = -7 + 7 + 3x + -3x + x2 + -1x2

Combine like terms: -7 + 7 = 0
4 + -1x + -1x2 = 0 + 3x + -3x + x2 + -1x2
4 + -1x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
4 + -1x + -1x2 = 0 + x2 + -1x2
4 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x + x2 = 0 + 4
x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
x + x2 = 4

The x term is x.  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.
 + 0.25 + x2 = 4 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
1.25 + x2 = 4.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + 0.5 = 2.061552813 Simplifying x + 0.5 = 2.061552813 Reorder the terms: 0.5 + x = 2.061552813 Solving 0.5 + x = 2.061552813 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 = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.061552813 + -0.5 x = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 x = 1.561552813 Simplifying x = 1.561552813

Subproblem 2

x + 0.5 = -2.061552813 Simplifying x + 0.5 = -2.061552813 Reorder the terms: 0.5 + x = -2.061552813 Solving 0.5 + x = -2.061552813 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 = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.061552813 + -0.5 x = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 x = -2.561552813 Simplifying x = -2.561552813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.561552813, -2.561552813}

See similar equations:

| 3+2h=3+5h | | .3-(.9+9k)= | | -5u=-6u-9 | | 9x-2x+66=9x+32 | | 9-77Y=32 | | (9*3-5)+15*2=x | | -5=-6u-9 | | -4p=24 | | 39x+16=39x+80 | | 5xy+2x= | | 100*t=6.5916 | | 0.6n=-6 | | 6x^2+8xy-14y^2=0 | | d=9.1cm | | -9-2t=-3t | | 5(k-4)-4(k+2)-14=-33 | | 3x+8y+66=360 | | 2log(1+3x)=6 | | 9-2t=3t | | 16y-32= | | 4[(5-1)3-(-4)]-53= | | 2(3x+2y)-3(x+y)= | | 4x^3+2x^2+12x+6=0 | | 4x^3+2x^2+12+-6=0 | | 4(n+7)-2(n+3)=-15n | | 4a-6+6a= | | 9x-(6x+2)=9x-50 | | 2n+3=-5 | | 18x+4y=44 | | 40=7.5*x | | (7x-3)+(11y+5)+x=180 | | 3p+4p=-25-4 |

Equations solver categories