4x^2+6x-21=0

Simple and best practice solution for 4x^2+6x-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 4x^2+6x-21=0 equation:


Simplifying
4x2 + 6x + -21 = 0

Reorder the terms:
-21 + 6x + 4x2 = 0

Solving
-21 + 6x + 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'.
-5.25 + 1.5x + x2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + 1.5x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + 1.5x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + 1.5x + x2 = 0 + 5.25
1.5x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
1.5x + x2 = 5.25

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 5.25 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 5.25 + 0.5625

Combine like terms: 5.25 + 0.5625 = 5.8125
0.5625 + 1.5x + x2 = 5.8125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 5.8125

Calculate the square root of the right side: 2.41091269

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.41091269 and -2.41091269.

Subproblem 1

x + 0.75 = 2.41091269 Simplifying x + 0.75 = 2.41091269 Reorder the terms: 0.75 + x = 2.41091269 Solving 0.75 + x = 2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.41091269 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.41091269 + -0.75 x = 2.41091269 + -0.75 Combine like terms: 2.41091269 + -0.75 = 1.66091269 x = 1.66091269 Simplifying x = 1.66091269

Subproblem 2

x + 0.75 = -2.41091269 Simplifying x + 0.75 = -2.41091269 Reorder the terms: 0.75 + x = -2.41091269 Solving 0.75 + x = -2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.41091269 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.41091269 + -0.75 x = -2.41091269 + -0.75 Combine like terms: -2.41091269 + -0.75 = -3.16091269 x = -3.16091269 Simplifying x = -3.16091269

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.66091269, -3.16091269}

See similar equations:

| 2a^2+12a+40=0 | | 3237=0.11a | | 8z-12=4z | | (3i)(-6i)= | | 4+ln(x+4)=6 | | 41x=-2747 | | 2(2x+5)=4x+8 | | 5y-(2-3y)=54 | | 8x-10-2x=-6x+10+9x | | 5x^2+24x+30=0 | | 19a-3(1-6)=66 | | y^2+6y+13=0 | | x^3+30x^2+225x= | | (Y-2)-(y+2)=4y | | 2y^3+14y^2-6y^2-42y= | | 4t^3-40t^2+100t=0 | | 2x-4=5x-10 | | p^2+2p=2.25 | | 5X+3=-3x-1 | | Y=2x^2-4x-3 | | 7+3x=-1-5x | | (30x^2y^2+5xy^2-15y^2)= | | 6x+4=6+4x | | (7-7)+12= | | x+7y=26 | | (5m)7= | | X^2+2x-1.5=0 | | z^2+x+42=0 | | 7(t-3)=2(c-9)+2t | | (30x^2y^2)+(5xy^2)-(15y^2)= | | 7(t-3)=2(c-9)+2c | | 6x^2-6x-36= |

Equations solver categories