10x^2+3x+17=180

Simple and best practice solution for 10x^2+3x+17=180 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 10x^2+3x+17=180 equation:


Simplifying
10x2 + 3x + 17 = 180

Reorder the terms:
17 + 3x + 10x2 = 180

Solving
17 + 3x + 10x2 = 180

Solving for variable 'x'.

Reorder the terms:
17 + -180 + 3x + 10x2 = 180 + -180

Combine like terms: 17 + -180 = -163
-163 + 3x + 10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-163 + 3x + 10x2 = 0

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

Divide each side by '10'.
-16.3 + 0.3x + x2 = 0

Move the constant term to the right:

Add '16.3' to each side of the equation.
-16.3 + 0.3x + 16.3 + x2 = 0 + 16.3

Reorder the terms:
-16.3 + 16.3 + 0.3x + x2 = 0 + 16.3

Combine like terms: -16.3 + 16.3 = 0.0
0.0 + 0.3x + x2 = 0 + 16.3
0.3x + x2 = 0 + 16.3

Combine like terms: 0 + 16.3 = 16.3
0.3x + x2 = 16.3

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 16.3 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 16.3 + 0.0225

Combine like terms: 16.3 + 0.0225 = 16.3225
0.0225 + 0.3x + x2 = 16.3225

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 16.3225

Calculate the square root of the right side: 4.040111385

Break this problem into two subproblems by setting 
(x + 0.15) equal to 4.040111385 and -4.040111385.

Subproblem 1

x + 0.15 = 4.040111385 Simplifying x + 0.15 = 4.040111385 Reorder the terms: 0.15 + x = 4.040111385 Solving 0.15 + x = 4.040111385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 4.040111385 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 4.040111385 + -0.15 x = 4.040111385 + -0.15 Combine like terms: 4.040111385 + -0.15 = 3.890111385 x = 3.890111385 Simplifying x = 3.890111385

Subproblem 2

x + 0.15 = -4.040111385 Simplifying x + 0.15 = -4.040111385 Reorder the terms: 0.15 + x = -4.040111385 Solving 0.15 + x = -4.040111385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -4.040111385 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -4.040111385 + -0.15 x = -4.040111385 + -0.15 Combine like terms: -4.040111385 + -0.15 = -4.190111385 x = -4.190111385 Simplifying x = -4.190111385

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.890111385, -4.190111385}

See similar equations:

| r^2-16r+60=0 | | x^10/x^2 | | y=-5/x | | 1.63q=9.63 | | -2/5-2/5=-2/5w+1/5w | | -7p+7+8p=9 | | 3c+30=m | | ln(x-3)+ln(x-2)=ln(6) | | -7x+x-7=-31 | | (ln)x+ln(x+2)=3 | | 4a+8=4+6a | | 5-2x=7x-h | | 4+7m-30-m=n | | (4-2p)=20 | | 4-2p=20 | | x+(x-6)+(x*3)=149 | | 6(3x+1)+3(1+6x)=9 | | 6x+10x=168 | | 2.5x-45=46-2x | | 10x=9y+9 | | 2(x-13)=3x | | 8/21.7/10 | | 13z-8=2x-15 | | 0=10x^3-15x^2-2x-3 | | 25t^2-100t+100=0 | | 6000=xsuare+40x | | g^2-11g=0 | | 5b^2-1=319 | | M+0.7=7 | | 4x^2-41x+21=0 | | 13x-19y=11 | | 32x^3-16x^2+2x=0 |

Equations solver categories