-7a^2-6a+21=0

Simple and best practice solution for -7a^2-6a+21=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 -7a^2-6a+21=0 equation:


Simplifying
-7a2 + -6a + 21 = 0

Reorder the terms:
21 + -6a + -7a2 = 0

Solving
21 + -6a + -7a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-3 + 0.8571428571a + a2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 0.8571428571a + 3 + a2 = 0 + 3

Reorder the terms:
-3 + 3 + 0.8571428571a + a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 0.8571428571a + a2 = 0 + 3
0.8571428571a + a2 = 0 + 3

Combine like terms: 0 + 3 = 3
0.8571428571a + a2 = 3

The a term is 0.8571428571a.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571a + 0.1836734694 + a2 = 3 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571a + a2 = 3 + 0.1836734694

Combine like terms: 3 + 0.1836734694 = 3.1836734694
0.1836734694 + 0.8571428571a + a2 = 3.1836734694

Factor a perfect square on the left side:
(a + 0.4285714286)(a + 0.4285714286) = 3.1836734694

Calculate the square root of the right side: 1.784285142

Break this problem into two subproblems by setting 
(a + 0.4285714286) equal to 1.784285142 and -1.784285142.

Subproblem 1

a + 0.4285714286 = 1.784285142 Simplifying a + 0.4285714286 = 1.784285142 Reorder the terms: 0.4285714286 + a = 1.784285142 Solving 0.4285714286 + a = 1.784285142 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + a = 1.784285142 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + a = 1.784285142 + -0.4285714286 a = 1.784285142 + -0.4285714286 Combine like terms: 1.784285142 + -0.4285714286 = 1.3557137134 a = 1.3557137134 Simplifying a = 1.3557137134

Subproblem 2

a + 0.4285714286 = -1.784285142 Simplifying a + 0.4285714286 = -1.784285142 Reorder the terms: 0.4285714286 + a = -1.784285142 Solving 0.4285714286 + a = -1.784285142 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + a = -1.784285142 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + a = -1.784285142 + -0.4285714286 a = -1.784285142 + -0.4285714286 Combine like terms: -1.784285142 + -0.4285714286 = -2.2128565706 a = -2.2128565706 Simplifying a = -2.2128565706

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.3557137134, -2.2128565706}

See similar equations:

| 6(4z-1)-3(z+7)=14(z+1) | | 6x+5-9x= | | -4(t-8)-(t+3)=6 | | (8t-2)=3(t+1)+3 | | 9+4(x-1)=8-2(x-5) | | w^2+1.113w=0 | | 28=0.55*32.5*(1-0.5w) | | 2(6z-1)-5(z+6)=3(z+1) | | 8.9375w^2+10.125w=0 | | -4x+14=-2 | | w^2+1.133w=0 | | 9-7x=54-42x | | -2=2x+7 | | 3(t-4)=2(t+3)+14 | | 7m=8 | | (2x+1)(x+6)= | | 2(x-2)+2(x-2)=18 | | 4p-3p=11-7 | | 3x+31=12x-50 | | 6.2=-4.83+y | | 75-6x=30x+19 | | q-2.78=4.2 | | 7X+2=32-3X | | 192=(x+2)(x+4) | | 11-n+3=3n+2n | | 9a+12a^2-5a= | | 2x=5y+30 | | 4y=5-x | | 52-x^2+x=10 | | -x^2+x-42=0 | | 7y=3+5y-8 | | 3x+3=-2x-(-2)-4 |

Equations solver categories