x^2+37x+53=0

Simple and best practice solution for x^2+37x+53=0 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+37x+53=0 equation:


Simplifying
x2 + 37x + 53 = 0

Reorder the terms:
53 + 37x + x2 = 0

Solving
53 + 37x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-53' to each side of the equation.
53 + 37x + -53 + x2 = 0 + -53

Reorder the terms:
53 + -53 + 37x + x2 = 0 + -53

Combine like terms: 53 + -53 = 0
0 + 37x + x2 = 0 + -53
37x + x2 = 0 + -53

Combine like terms: 0 + -53 = -53
37x + x2 = -53

The x term is 37x.  Take half its coefficient (18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
37x + 342.25 + x2 = -53 + 342.25

Reorder the terms:
342.25 + 37x + x2 = -53 + 342.25

Combine like terms: -53 + 342.25 = 289.25
342.25 + 37x + x2 = 289.25

Factor a perfect square on the left side:
(x + 18.5)(x + 18.5) = 289.25

Calculate the square root of the right side: 17.007351352

Break this problem into two subproblems by setting 
(x + 18.5) equal to 17.007351352 and -17.007351352.

Subproblem 1

x + 18.5 = 17.007351352 Simplifying x + 18.5 = 17.007351352 Reorder the terms: 18.5 + x = 17.007351352 Solving 18.5 + x = 17.007351352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 17.007351352 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 17.007351352 + -18.5 x = 17.007351352 + -18.5 Combine like terms: 17.007351352 + -18.5 = -1.492648648 x = -1.492648648 Simplifying x = -1.492648648

Subproblem 2

x + 18.5 = -17.007351352 Simplifying x + 18.5 = -17.007351352 Reorder the terms: 18.5 + x = -17.007351352 Solving 18.5 + x = -17.007351352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -17.007351352 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -17.007351352 + -18.5 x = -17.007351352 + -18.5 Combine like terms: -17.007351352 + -18.5 = -35.507351352 x = -35.507351352 Simplifying x = -35.507351352

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.492648648, -35.507351352}

See similar equations:

| 4(x-6)-(4x+24)=0 | | 5x+30=6x-10 | | y=5-0 | | 3(1y+2)+2(1y-3)=-15 | | x=0.029sin(14t) | | 4y-2(1y-5)=2 | | 12x+4=10x+6 | | -4x+5=x-25 | | 6x-12=5x+10 | | 6=t/5- | | 3(x+4)-6=3x+6 | | 7y-3(1y+6)=10 | | 60+(x+20)+x=180 | | 2y+9x=160 | | 2v+5v+-8=13 | | (2x+4)+(7x-8)=180 | | 2/3=-9 | | C=2pr | | 3y+3(1-1y)-1y=6 | | 2(x+3)=6+2x | | ln(x)+ln(x-4)=ln(24) | | (X+20)+3x=120 | | 2x+3-12=180 | | 23x+7-26x=5-7 | | 2x+1-3x-5=3x-4x-6 | | 4y=12.8 | | 2x+2=9x+30 | | 3/4*6+1/2=1/2*6 | | 7(2x-6)=5(x+6) | | 5y+4(y-2)=6-y | | 3/4*5+1/2=1/2*5 | | -5(-6x-5)=115 |

Equations solver categories