3x^2-7=5x

Simple and best practice solution for 3x^2-7=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 3x^2-7=5x equation:


Simplifying
3x2 + -7 = 5x

Reorder the terms:
-7 + 3x2 = 5x

Solving
-7 + 3x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-7 + -5x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-7 + -5x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -1.666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -1.666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + 2.333333333
-1.666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-1.666666667x + x2 = 2.333333333

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 2.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 2.333333333 + 0.6944444447

Combine like terms: 2.333333333 + 0.6944444447 = 3.0277777777
0.6944444447 + -1.666666667x + x2 = 3.0277777777

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 3.0277777777

Calculate the square root of the right side: 1.740051085

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.740051085 and -1.740051085.

Subproblem 1

x + -0.8333333335 = 1.740051085 Simplifying x + -0.8333333335 = 1.740051085 Reorder the terms: -0.8333333335 + x = 1.740051085 Solving -0.8333333335 + x = 1.740051085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.740051085 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.740051085 + 0.8333333335 x = 1.740051085 + 0.8333333335 Combine like terms: 1.740051085 + 0.8333333335 = 2.5733844185 x = 2.5733844185 Simplifying x = 2.5733844185

Subproblem 2

x + -0.8333333335 = -1.740051085 Simplifying x + -0.8333333335 = -1.740051085 Reorder the terms: -0.8333333335 + x = -1.740051085 Solving -0.8333333335 + x = -1.740051085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.740051085 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.740051085 + 0.8333333335 x = -1.740051085 + 0.8333333335 Combine like terms: -1.740051085 + 0.8333333335 = -0.9067177515 x = -0.9067177515 Simplifying x = -0.9067177515

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.5733844185, -0.9067177515}

See similar equations:

| 5x+4y+23=0 | | .2x+5=8 | | -9x-2=-6x-14 | | 12=4-2y | | 4(2x-3)=28 | | 2x+193=11x-5 | | 162=3(x+6)(x+3) | | -45x^3+111x^2=0 | | -2w=-18 | | 58-3x=24x+19 | | (7x^2-4x+1)+(3x^2-9x-5)= | | 2x+1=5-4x | | -17p-11+2p^2=-2p^2+9p+3 | | 49-5x=13x+17 | | 7(x-2)=49 | | 15w+50=400 | | 20x^3+15x=0 | | 25w+50=50 | | 6x^2-13x=0 | | 3x^2-6kx+12=0 | | 408=s-129 | | 91-5x=7x-19 | | 3r^2+11r+10=0 | | 1204=w+389 | | 162=x(x+3)(x-3) | | M+45=123 | | 3a(5x+y)-(-y-5x)=0 | | 6x-40=4 | | 8x+5y=4 | | .02(8.5y-2)=.5 | | 33+45=x | | 8x+4=3x-26 |

Equations solver categories