10x^2-7x-4=0

Simple and best practice solution for 10x^2-7x-4=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 10x^2-7x-4=0 equation:


Simplifying
10x2 + -7x + -4 = 0

Reorder the terms:
-4 + -7x + 10x2 = 0

Solving
-4 + -7x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-0.4 + -0.7x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -0.7x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -0.7x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -0.7x + x2 = 0 + 0.4
-0.7x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-0.7x + x2 = 0.4

The x term is -0.7x.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7x + 0.1225 + x2 = 0.4 + 0.1225

Reorder the terms:
0.1225 + -0.7x + x2 = 0.4 + 0.1225

Combine like terms: 0.4 + 0.1225 = 0.5225
0.1225 + -0.7x + x2 = 0.5225

Factor a perfect square on the left side:
(x + -0.35)(x + -0.35) = 0.5225

Calculate the square root of the right side: 0.722841615

Break this problem into two subproblems by setting 
(x + -0.35) equal to 0.722841615 and -0.722841615.

Subproblem 1

x + -0.35 = 0.722841615 Simplifying x + -0.35 = 0.722841615 Reorder the terms: -0.35 + x = 0.722841615 Solving -0.35 + x = 0.722841615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 0.722841615 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.722841615 + 0.35 x = 0.722841615 + 0.35 Combine like terms: 0.722841615 + 0.35 = 1.072841615 x = 1.072841615 Simplifying x = 1.072841615

Subproblem 2

x + -0.35 = -0.722841615 Simplifying x + -0.35 = -0.722841615 Reorder the terms: -0.35 + x = -0.722841615 Solving -0.35 + x = -0.722841615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -0.722841615 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -0.722841615 + 0.35 x = -0.722841615 + 0.35 Combine like terms: -0.722841615 + 0.35 = -0.372841615 x = -0.372841615 Simplifying x = -0.372841615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.072841615, -0.372841615}

See similar equations:

| 5x+27=14x-45 | | -26=6(6w-6)-8w | | 5x+27=14x-5 | | 5x^2+17=97 | | w^2+3w+2=0 | | x+21+2x=-16-2x-23 | | 3x-21=0 | | 5x^2-14x=3 | | 8y-2(3y+1)=2y+7 | | 6x+4=-14 | | 10y=9x-8 | | 2t^5(t-t^2+7t^3)=0 | | 7-4x=-21 | | 2x+3=3x-2 | | 4u^2-6=-5u | | 3x-8=4x+5 | | 12x+14=31x-43 | | 5-4x=-3 | | X^2-27x=0 | | 0.45x+.05(14-x)=.10(23) | | 8x+6=6x-7x+24 | | qx+rs=s | | 16x-28=-28+16x | | m^2-11m+28=0 | | 178-3x=33x+18 | | 2(4t-5)=40-t | | -3(x+4)-43=6-34 | | 4x-20x+64=0 | | 7x+14-6x=-2-12 | | 2x+6=2# | | 6x=2(5x+14) | | 26+10y=30+8y |

Equations solver categories