x^2-4x-7=0

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


Simplifying
x2 + -4x + -7 = 0

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

Solving
-7 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -4x + 7 + x2 = 0 + 7

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

Combine like terms: -7 + 7 = 0
0 + -4x + x2 = 0 + 7
-4x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-4x + x2 = 7

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 7 + 4

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

Combine like terms: 7 + 4 = 11
4 + -4x + x2 = 11

Factor a perfect square on the left side:
(x + -2)(x + -2) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -2) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -2 = 3.31662479 Simplifying x + -2 = 3.31662479 Reorder the terms: -2 + x = 3.31662479 Solving -2 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.31662479 + 2 x = 3.31662479 + 2 Combine like terms: 3.31662479 + 2 = 5.31662479 x = 5.31662479 Simplifying x = 5.31662479

Subproblem 2

x + -2 = -3.31662479 Simplifying x + -2 = -3.31662479 Reorder the terms: -2 + x = -3.31662479 Solving -2 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.31662479 + 2 x = -3.31662479 + 2 Combine like terms: -3.31662479 + 2 = -1.31662479 x = -1.31662479 Simplifying x = -1.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.31662479, -1.31662479}

See similar equations:

| y=-11x-3 | | 5x^2=6+2x | | -2x+4(2x-4)=-1-9x | | 5x+2=6x-11 | | -5y-12x=-5 | | 4(y^2-33)=-37y | | 12y=4x-7 | | 5x^2+28x+32=0 | | 4+2X=10+X | | 2x-(5x+2)=13 | | 4x-1800=x+1800 | | 2x^2+12x+16=0 | | Y=10+1(2) | | Y=10+1(0) | | 2y-8=6-7y | | Y=4+2(1) | | 3(x+4)=72 | | 9.47=7.45x-8.81 | | 4(1-x)-(4+x)=14 | | y=(x-1)(4x+2)-4x^2 | | a^2=7 | | 16x^2-26x-35=0 | | 5(x+3)=119-8x | | 4x^3-11x^2-43x-10=0(x-5) | | 4x^2-22x=0 | | 9n=126 | | 4x^4+9x^2+2=0 | | 7x+4=-24 | | -7x+17=-16 | | 13+9p=10p | | x^4-8x^2-9=0 | | -y^2+12y-19=18x-x |

Equations solver categories