45x-16x^2=10

Simple and best practice solution for 45x-16x^2=10 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 45x-16x^2=10 equation:


Simplifying
45x + -16x2 = 10

Solving
45x + -16x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 45x + -16x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 45x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.625 + -2.8125x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -2.8125x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -2.8125x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -2.8125x + x2 = 0 + -0.625
-2.8125x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-2.8125x + x2 = -0.625

The x term is -2.8125x.  Take half its coefficient (-1.40625).
Square it (1.977539063) and add it to both sides.

Add '1.977539063' to each side of the equation.
-2.8125x + 1.977539063 + x2 = -0.625 + 1.977539063

Reorder the terms:
1.977539063 + -2.8125x + x2 = -0.625 + 1.977539063

Combine like terms: -0.625 + 1.977539063 = 1.352539063
1.977539063 + -2.8125x + x2 = 1.352539063

Factor a perfect square on the left side:
(x + -1.40625)(x + -1.40625) = 1.352539063

Calculate the square root of the right side: 1.162987129

Break this problem into two subproblems by setting 
(x + -1.40625) equal to 1.162987129 and -1.162987129.

Subproblem 1

x + -1.40625 = 1.162987129 Simplifying x + -1.40625 = 1.162987129 Reorder the terms: -1.40625 + x = 1.162987129 Solving -1.40625 + x = 1.162987129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = 1.162987129 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = 1.162987129 + 1.40625 x = 1.162987129 + 1.40625 Combine like terms: 1.162987129 + 1.40625 = 2.569237129 x = 2.569237129 Simplifying x = 2.569237129

Subproblem 2

x + -1.40625 = -1.162987129 Simplifying x + -1.40625 = -1.162987129 Reorder the terms: -1.40625 + x = -1.162987129 Solving -1.40625 + x = -1.162987129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = -1.162987129 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = -1.162987129 + 1.40625 x = -1.162987129 + 1.40625 Combine like terms: -1.162987129 + 1.40625 = 0.243262871 x = 0.243262871 Simplifying x = 0.243262871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.569237129, 0.243262871}

See similar equations:

| 2x^2+4xy+2y^2-5x+4y+7=0 | | 4x-B(x+1)(x+1)+4x=4-Bx^2 | | -6x-6+8x=2x-6 | | 17-7=-32 | | 75c^2+90cd+27d^2=0 | | 4-6x=-x-11 | | 3x^2=7x+10 | | 400=(5000)(4)(x) | | 7+6n=-11 | | 5u+5-7=3u-3+2u | | 5n-(n+3)=n+2+7 | | 3G+21=20+2g | | 2(2-x)=3(x+5) | | 9.99+1.5n=36.99 | | 3x^2=7x-10 | | 7+4y-9=-6 | | 7m+11-5m-2=3k-6 | | 5x-10=3x+2corta | | 5n+9=x-23 | | m-9=11-4m | | (2x+20)+4x=90 | | 5x+10+x=3x-3+1 | | 4.18x+1.56=3.4x | | N^2-n-5852=0 | | 160=(2)(8)(x) | | 0.5-3t+5=o | | 7+2x=4(2x+2)-7(x-3) | | 8x^2y-50y= | | 3y=5.5 | | 0.5x^2-0.4x-1.2= | | 9+9p-4=8p+30-4p | | 6(x+3)+2=3x+3(5+x) |

Equations solver categories