3.5(3.5+28)=x(x+14)

Simple and best practice solution for 3.5(3.5+28)=x(x+14) 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 3.5(3.5+28)=x(x+14) equation:


Simplifying
3.5(3.5 + 28) = x(x + 14)

Combine like terms: 3.5 + 28 = 31.5
3.5(31.5) = x(x + 14)

Multiply 3.5 * 31.5
110.25 = x(x + 14)

Reorder the terms:
110.25 = x(14 + x)
110.25 = (14 * x + x * x)
110.25 = (14x + x2)

Solving
110.25 = 14x + x2

Solving for variable 'x'.

Reorder the terms:
110.25 + -14x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
110.25 + -14x + -1x2 = 0 + x2 + -1x2
110.25 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
110.25 + -14x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-110.25 + 14x + x2 = 0

Move the constant term to the right:

Add '110.25' to each side of the equation.
-110.25 + 14x + 110.25 + x2 = 0 + 110.25

Reorder the terms:
-110.25 + 110.25 + 14x + x2 = 0 + 110.25

Combine like terms: -110.25 + 110.25 = 0.00
0.00 + 14x + x2 = 0 + 110.25
14x + x2 = 0 + 110.25

Combine like terms: 0 + 110.25 = 110.25
14x + x2 = 110.25

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 110.25 + 49

Reorder the terms:
49 + 14x + x2 = 110.25 + 49

Combine like terms: 110.25 + 49 = 159.25
49 + 14x + x2 = 159.25

Factor a perfect square on the left side:
(x + 7)(x + 7) = 159.25

Calculate the square root of the right side: 12.619429464

Break this problem into two subproblems by setting 
(x + 7) equal to 12.619429464 and -12.619429464.

Subproblem 1

x + 7 = 12.619429464 Simplifying x + 7 = 12.619429464 Reorder the terms: 7 + x = 12.619429464 Solving 7 + x = 12.619429464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 12.619429464 + -7 Combine like terms: 7 + -7 = 0 0 + x = 12.619429464 + -7 x = 12.619429464 + -7 Combine like terms: 12.619429464 + -7 = 5.619429464 x = 5.619429464 Simplifying x = 5.619429464

Subproblem 2

x + 7 = -12.619429464 Simplifying x + 7 = -12.619429464 Reorder the terms: 7 + x = -12.619429464 Solving 7 + x = -12.619429464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -12.619429464 + -7 Combine like terms: 7 + -7 = 0 0 + x = -12.619429464 + -7 x = -12.619429464 + -7 Combine like terms: -12.619429464 + -7 = -19.619429464 x = -19.619429464 Simplifying x = -19.619429464

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.619429464, -19.619429464}

See similar equations:

| 9x2/15 | | 3a-7a=12 | | 6m+12=3(2m+8) | | 3a+7a=12 | | 4m-4=4(m-1) | | -16t^2-484=0 | | 5x-3=2a | | 2a^3b-10a^2b^2+12ab^3=0 | | 0.5x^2+x=0 | | -(6x-7)+2(3x-4)=3 | | 7y-3=6x-18 | | 26x-6-17x+3=20x-4-11x+17 | | -1(x-7)=-9 | | 2-x=4x+1 | | 5(3x+4)-2x=7-3(-2x+11) | | 15q^2-7q-4=0 | | -3(n-6)=-2(n-6) | | 16+X^2-2x=13 | | x/5-21 | | 20x^2+39x-11=0 | | 0.1(5b+85)=0.5+8.6 | | (5x+3)(3x+7)=abc | | 9(4-v)= | | 2(x+50)-30=15 | | 4y=5x+19 | | (5x+3)(3x+7)=180 | | (5x+3)(3x+7)=90 | | 20r^2-28r-3=0 | | 7d+77=3d-75 | | (5x-22)(4x+4)=90 | | 20-3(2x-1)=-5x+6 | | 6t^2+t-1=0 |

Equations solver categories