4x^2-42x+45=0

Simple and best practice solution for 4x^2-42x+45=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 4x^2-42x+45=0 equation:


Simplifying
4x2 + -42x + 45 = 0

Reorder the terms:
45 + -42x + 4x2 = 0

Solving
45 + -42x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
11.25 + -10.5x + x2 = 0

Move the constant term to the right:

Add '-11.25' to each side of the equation.
11.25 + -10.5x + -11.25 + x2 = 0 + -11.25

Reorder the terms:
11.25 + -11.25 + -10.5x + x2 = 0 + -11.25

Combine like terms: 11.25 + -11.25 = 0.00
0.00 + -10.5x + x2 = 0 + -11.25
-10.5x + x2 = 0 + -11.25

Combine like terms: 0 + -11.25 = -11.25
-10.5x + x2 = -11.25

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -11.25 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -11.25 + 27.5625

Combine like terms: -11.25 + 27.5625 = 16.3125
27.5625 + -10.5x + x2 = 16.3125

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 16.3125

Calculate the square root of the right side: 4.038873605

Break this problem into two subproblems by setting 
(x + -5.25) equal to 4.038873605 and -4.038873605.

Subproblem 1

x + -5.25 = 4.038873605 Simplifying x + -5.25 = 4.038873605 Reorder the terms: -5.25 + x = 4.038873605 Solving -5.25 + x = 4.038873605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 4.038873605 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.038873605 + 5.25 x = 4.038873605 + 5.25 Combine like terms: 4.038873605 + 5.25 = 9.288873605 x = 9.288873605 Simplifying x = 9.288873605

Subproblem 2

x + -5.25 = -4.038873605 Simplifying x + -5.25 = -4.038873605 Reorder the terms: -5.25 + x = -4.038873605 Solving -5.25 + x = -4.038873605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -4.038873605 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.038873605 + 5.25 x = -4.038873605 + 5.25 Combine like terms: -4.038873605 + 5.25 = 1.211126395 x = 1.211126395 Simplifying x = 1.211126395

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.288873605, 1.211126395}

See similar equations:

| 5=-5(-29)+4 | | 6(z-7)=3 | | -8x+14=-2[4x-7] | | 7z=-35 | | -0.75(z+0.17)=0.2(z-0.375) | | 8a-9a=7a-6 | | 2x-3x=-4 | | 2=-5(14)+4 | | 5.3-2.1x=-8.14 | | 4.1m-8.6=2.47 | | -56=6(p+4)-4(1-8p) | | 2(1+2x)=3(x-3) | | 7x+3y=11x-5y | | -0.03-0.9w=2.4 | | 5-c=8 | | 1/3(y+2)=3y-5(y-2) | | 0.05x+0.037=0.262 | | 6x-(3x-4)=14 | | -2z=18 | | 0.3x+0.4+x=2x-10 | | 1.7w-0.44=5 | | 2t-t=22-t | | 9+4n-1=9n+9-4n | | -0.24y+0.14=3.2 | | -5(n-4)-6(8n-5)=-3 | | 2x-60=4x-70 | | 0.1x=0.3x-7 | | -3x+6=-5x-6 | | 3x-4=-2x^2+x+1 | | -5(n-4)-6(8n-6)=-3 | | 4(x-6)=4x-6 | | -5(0.2x+0.1)-0.6=1.9 |

Equations solver categories