52=4x^2+5x

Simple and best practice solution for 52=4x^2+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 52=4x^2+5x equation:


Simplifying
52 = 4x2 + 5x

Reorder the terms:
52 = 5x + 4x2

Solving
52 = 5x + 4x2

Solving for variable 'x'.

Reorder the terms:
52 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
52 + -5x + -4x2 = 0 + 4x2 + -4x2
52 + -5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
52 + -5x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-13 + 1.25x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 1.25x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 1.25x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 1.25x + x2 = 0 + 13
1.25x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
1.25x + x2 = 13

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 13 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 13 + 0.390625

Combine like terms: 13 + 0.390625 = 13.390625
0.390625 + 1.25x + x2 = 13.390625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 13.390625

Calculate the square root of the right side: 3.659320292

Break this problem into two subproblems by setting 
(x + 0.625) equal to 3.659320292 and -3.659320292.

Subproblem 1

x + 0.625 = 3.659320292 Simplifying x + 0.625 = 3.659320292 Reorder the terms: 0.625 + x = 3.659320292 Solving 0.625 + x = 3.659320292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 3.659320292 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.659320292 + -0.625 x = 3.659320292 + -0.625 Combine like terms: 3.659320292 + -0.625 = 3.034320292 x = 3.034320292 Simplifying x = 3.034320292

Subproblem 2

x + 0.625 = -3.659320292 Simplifying x + 0.625 = -3.659320292 Reorder the terms: 0.625 + x = -3.659320292 Solving 0.625 + x = -3.659320292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -3.659320292 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.659320292 + -0.625 x = -3.659320292 + -0.625 Combine like terms: -3.659320292 + -0.625 = -4.284320292 x = -4.284320292 Simplifying x = -4.284320292

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.034320292, -4.284320292}

See similar equations:

| (x+9)+(x+3)+(x+6)=(x+4)+(x+1) | | 22-6y=18 | | -10v=30 | | -9=7+w | | 2x^2-7x+2= | | 3u-14=13 | | 12x+4x+12y+6y=0 | | =100+36q-4q^2 | | 54=16t^2 | | 9+2x-3=7 | | 20=16t^2 | | 5u+1-4(-2u-2)=3(u-1) | | 5a+3b=39 | | 4(v-3)-2=-3(-7v+2)-3v | | 58x=8x | | -2(4w-7)+4w=5(w+4) | | 84=-6y | | (2y^2+3x)*dx+2xy*dy=0 | | d=344.9 | | -36-9x=-5 | | 17+3k=6k-8 | | d=344(.09) | | 4.5v=40 | | 9x^2+kx+k=0 | | 0.5x+10=25 | | Y=ln(5-9x) | | 74=-4x+2(7x-13) | | 10+3z=7(z-2) | | X^2+y-25=0 | | .4(x+7)=.6(x-4.2) | | z^3+(1-3i)z^2-(2+3i)z-2=0 | | 3x^2-10xy+3y^2+22x-26y+43=0 |

Equations solver categories