0=-x^2+3x+1

Simple and best practice solution for 0=-x^2+3x+1 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 0=-x^2+3x+1 equation:


Simplifying
0 = -1x2 + 3x + 1

Reorder the terms:
0 = 1 + 3x + -1x2

Solving
0 = 1 + 3x + -1x2

Solving for variable 'x'.

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

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3x + x2 = 0 + 1

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

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

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 = 1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3x + x2 = 3.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

x + -1.5 = 1.802775638 Simplifying x + -1.5 = 1.802775638 Reorder the terms: -1.5 + x = 1.802775638 Solving -1.5 + x = 1.802775638 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 = 1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.802775638 + 1.5 x = 1.802775638 + 1.5 Combine like terms: 1.802775638 + 1.5 = 3.302775638 x = 3.302775638 Simplifying x = 3.302775638

Subproblem 2

x + -1.5 = -1.802775638 Simplifying x + -1.5 = -1.802775638 Reorder the terms: -1.5 + x = -1.802775638 Solving -1.5 + x = -1.802775638 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 = -1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.802775638 + 1.5 x = -1.802775638 + 1.5 Combine like terms: -1.802775638 + 1.5 = -0.302775638 x = -0.302775638 Simplifying x = -0.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.302775638, -0.302775638}

See similar equations:

| -5=3n-8(6+5n) | | 50+60=470 | | -4(2x+8)=14x-8 | | 3t^2-33t=90 | | k-9/k+3=6/5 | | 11(c-4)+8=2+c-38 | | 97=y+155 | | 4p+9q-2p-3q= | | 9n+3=30 | | 3(2x-3)=-21 | | r+6=-4 | | 3c-15=-18 | | 8h-6=42 | | y-7=b | | -24+3k=k-6k | | E(c+b)=d | | 5-3k=-5(5k-1) | | b(b+32)=9(5+4b) | | 20x=-2x-8x | | -6p=-192 | | 2x^2-1.5x-0.5=0 | | (1/2)x+(1/4)x=16 | | 9p-11p=-10p | | b^3+a^2+b^2-a^3-2ab=0 | | M-15=-4 | | 2(1-4n)=-(1+5n) | | 4x-(3/5)=(2/5) | | -5y+1=3 | | 1.2t=4.6 | | 756x=12 | | 7y+3=8y-4 | | 5.25x+2=16.5x+11 |

Equations solver categories