x^2+1=3x+7

Simple and best practice solution for x^2+1=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 x^2+1=3x+7 equation:


Simplifying
x2 + 1 = 3x + 7

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

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

Solving
1 + x2 = 7 + 3x

Solving for variable 'x'.

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

Combine like terms: 1 + -7 = -6
-6 + -3x + x2 = 7 + 3x + -7 + -3x

Reorder the terms:
-6 + -3x + x2 = 7 + -7 + 3x + -3x

Combine like terms: 7 + -7 = 0
-6 + -3x + x2 = 0 + 3x + -3x
-6 + -3x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-6 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -3x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -3x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -3x + x2 = 0 + 6
-3x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-3x + x2 = 6

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 6 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + -3x + x2 = 8.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

x + -1.5 = 2.872281323 Simplifying x + -1.5 = 2.872281323 Reorder the terms: -1.5 + x = 2.872281323 Solving -1.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.872281323 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.872281323 + 1.5 x = 2.872281323 + 1.5 Combine like terms: 2.872281323 + 1.5 = 4.372281323 x = 4.372281323 Simplifying x = 4.372281323

Subproblem 2

x + -1.5 = -2.872281323 Simplifying x + -1.5 = -2.872281323 Reorder the terms: -1.5 + x = -2.872281323 Solving -1.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.872281323 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.872281323 + 1.5 x = -2.872281323 + 1.5 Combine like terms: -2.872281323 + 1.5 = -1.372281323 x = -1.372281323 Simplifying x = -1.372281323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.372281323, -1.372281323}

See similar equations:

| 18x^2-9x-14= | | -5t^2+100t-480=0 | | 0.4x-2.2=1.4 | | 2c^2+11c+5= | | 1.6+60=110 | | 4(3x+4)+1=-7 | | 54=(x+10)(2x-3) | | 4(3x+4)+1=7 | | 3x^3+12x^2y^2-96xy^3= | | (16x+4)-36=0 | | -5t^2-20t+96=0 | | -7x+1=-x+1 | | (16x+4)=36 | | 60+1.6Y=176 | | 11+12m+m^2= | | X(2-x)+b(2-b)=5 | | 2x^2+17x-84=0 | | 9x=4-7x | | x^2+29x+17= | | 7q^2-2pq-7q+2p= | | X=110+-1Y | | 1.6X+1.6Y=176 | | (X+15)+x+39=180 | | y(x-8)-5(x-8)= | | 2x+2b=5 | | -32xy-98x^2= | | 2(3b^2+2)+4b-5= | | 6x^2+12x-48= | | 12p^2=8-10p | | R*1.6(R+10)*1.6=176 | | 2(2x+3)=2x-12 | | 2x-4(x-2)=2x+4 |

Equations solver categories