5x^2+16x-46=0

Simple and best practice solution for 5x^2+16x-46=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 5x^2+16x-46=0 equation:


Simplifying
5x2 + 16x + -46 = 0

Reorder the terms:
-46 + 16x + 5x2 = 0

Solving
-46 + 16x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-9.2 + 3.2x + x2 = 0

Move the constant term to the right:

Add '9.2' to each side of the equation.
-9.2 + 3.2x + 9.2 + x2 = 0 + 9.2

Reorder the terms:
-9.2 + 9.2 + 3.2x + x2 = 0 + 9.2

Combine like terms: -9.2 + 9.2 = 0.0
0.0 + 3.2x + x2 = 0 + 9.2
3.2x + x2 = 0 + 9.2

Combine like terms: 0 + 9.2 = 9.2
3.2x + x2 = 9.2

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = 9.2 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = 9.2 + 2.56

Combine like terms: 9.2 + 2.56 = 11.76
2.56 + 3.2x + x2 = 11.76

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 11.76

Calculate the square root of the right side: 3.42928564

Break this problem into two subproblems by setting 
(x + 1.6) equal to 3.42928564 and -3.42928564.

Subproblem 1

x + 1.6 = 3.42928564 Simplifying x + 1.6 = 3.42928564 Reorder the terms: 1.6 + x = 3.42928564 Solving 1.6 + x = 3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 3.42928564 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 3.42928564 + -1.6 x = 3.42928564 + -1.6 Combine like terms: 3.42928564 + -1.6 = 1.82928564 x = 1.82928564 Simplifying x = 1.82928564

Subproblem 2

x + 1.6 = -3.42928564 Simplifying x + 1.6 = -3.42928564 Reorder the terms: 1.6 + x = -3.42928564 Solving 1.6 + x = -3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -3.42928564 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -3.42928564 + -1.6 x = -3.42928564 + -1.6 Combine like terms: -3.42928564 + -1.6 = -5.02928564 x = -5.02928564 Simplifying x = -5.02928564

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.82928564, -5.02928564}

See similar equations:

| -18+31=20k | | -15+5m=8m+9 | | 96=8(x-8) | | 35x=105 | | 10a+20=5a+60 | | -4x=1 | | -2(-9+p)=-20 | | 8=n+4 | | 9(-3x+14)-8(5x-4)=-378 | | 9k+15=3k+45 | | -5a+6=9 | | x^3-3x^2-18=0 | | 2x=12y | | -2(x+7)=-22 | | 4(1-x)=3(2-x) | | 15x=8x-14x | | z^2-6z+25=0 | | -2(m+2)=-2 | | p+(p+4)=26 | | f(x-2)= | | 12-5x=x+6 | | n-35x=105 | | -173=10r-3 | | -7x+3(2x+5)=0.2(x-9)+4 | | 9x^2-8=-34x | | -2(n-4)=24 | | 100=3.14*(x+1)*(x+1) | | 7x+2(x-3)=5 | | 4c+3=2c+7 | | 4x^2-1-17=0 | | 7(4-2x)-6x=3 | | 21+-119=14x |

Equations solver categories