x^2+7x-45=7

Simple and best practice solution for x^2+7x-45=7 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+7x-45=7 equation:


Simplifying
x2 + 7x + -45 = 7

Reorder the terms:
-45 + 7x + x2 = 7

Solving
-45 + 7x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-45 + -7 + 7x + x2 = 7 + -7

Combine like terms: -45 + -7 = -52
-52 + 7x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-52 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + 7x + 52 + x2 = 0 + 52

Reorder the terms:
-52 + 52 + 7x + x2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 7x + x2 = 0 + 52
7x + x2 = 0 + 52

Combine like terms: 0 + 52 = 52
7x + x2 = 52

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 52 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 52 + 12.25

Combine like terms: 52 + 12.25 = 64.25
12.25 + 7x + x2 = 64.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(x + 3.5) equal to 8.015609771 and -8.015609771.

Subproblem 1

x + 3.5 = 8.015609771 Simplifying x + 3.5 = 8.015609771 Reorder the terms: 3.5 + x = 8.015609771 Solving 3.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 8.015609771 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 8.015609771 + -3.5 x = 8.015609771 + -3.5 Combine like terms: 8.015609771 + -3.5 = 4.515609771 x = 4.515609771 Simplifying x = 4.515609771

Subproblem 2

x + 3.5 = -8.015609771 Simplifying x + 3.5 = -8.015609771 Reorder the terms: 3.5 + x = -8.015609771 Solving 3.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -8.015609771 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -8.015609771 + -3.5 x = -8.015609771 + -3.5 Combine like terms: -8.015609771 + -3.5 = -11.515609771 x = -11.515609771 Simplifying x = -11.515609771

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.515609771, -11.515609771}

See similar equations:

| (x-3)(x^2+3x+9)= | | 5x+3y-12=0 | | 2(7+x)=48 | | 10x+12+x-10=x-5 | | 5n^2+19n-68=0 | | 9c+12-3c=c-2 | | n^2+13n+22=7 | | 2(3+2x)=26 | | ln(x-3)+ln(3x+1)=5 | | x^2+5x-54=0 | | 8y+5-y=4y+6 | | 5v^2-21=10 | | 3(3x-2)=75 | | z^3+125= | | -12x+8-6x=-9x+15-7x | | m^2+10m+14=-7 | | 26y^2-35y+9= | | -7-(-24/6)= | | -7-(24/6)= | | -7-(60/6)= | | -7-(-60/6)= | | 1+2x= | | -7-60/6= | | -2y^2+6y=2 | | -7--60/6= | | -7--60/6=3 | | 6x^2+21x-23=19-8x | | -7-24/6=3 | | 16x^4-41x^2+25=0 | | 6x-2-(-2x+3)= | | -3*2/3+-1*3/4= | | 6x^2-5x-66=0 |

Equations solver categories