4s^2=s+1

Simple and best practice solution for 4s^2=s+1 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 4s^2=s+1 equation:


Simplifying
4s2 = s + 1

Reorder the terms:
4s2 = 1 + s

Solving
4s2 = 1 + s

Solving for variable 's'.

Reorder the terms:
-1 + -1s + 4s2 = 1 + s + -1 + -1s

Reorder the terms:
-1 + -1s + 4s2 = 1 + -1 + s + -1s

Combine like terms: 1 + -1 = 0
-1 + -1s + 4s2 = 0 + s + -1s
-1 + -1s + 4s2 = s + -1s

Combine like terms: s + -1s = 0
-1 + -1s + 4s2 = 0

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

Divide each side by '4'.
-0.25 + -0.25s + s2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.25s + 0.25 + s2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.25s + s2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.25s + s2 = 0 + 0.25
-0.25s + s2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.25s + s2 = 0.25

The s term is -0.25s.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25s + 0.015625 + s2 = 0.25 + 0.015625

Reorder the terms:
0.015625 + -0.25s + s2 = 0.25 + 0.015625

Combine like terms: 0.25 + 0.015625 = 0.265625
0.015625 + -0.25s + s2 = 0.265625

Factor a perfect square on the left side:
(s + -0.125)(s + -0.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(s + -0.125) equal to 0.515388203 and -0.515388203.

Subproblem 1

s + -0.125 = 0.515388203 Simplifying s + -0.125 = 0.515388203 Reorder the terms: -0.125 + s = 0.515388203 Solving -0.125 + s = 0.515388203 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + s = 0.515388203 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + s = 0.515388203 + 0.125 s = 0.515388203 + 0.125 Combine like terms: 0.515388203 + 0.125 = 0.640388203 s = 0.640388203 Simplifying s = 0.640388203

Subproblem 2

s + -0.125 = -0.515388203 Simplifying s + -0.125 = -0.515388203 Reorder the terms: -0.125 + s = -0.515388203 Solving -0.125 + s = -0.515388203 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + s = -0.515388203 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + s = -0.515388203 + 0.125 s = -0.515388203 + 0.125 Combine like terms: -0.515388203 + 0.125 = -0.390388203 s = -0.390388203 Simplifying s = -0.390388203

Solution

The solution to the problem is based on the solutions from the subproblems. s = {0.640388203, -0.390388203}

See similar equations:

| -(8y+4)-(-7y-7)=-1 | | (2y-x+3z-13)-(4x+2-5y)+(6z+8)= | | 2.3-7x=-25.7 | | s^2=1+s(1-3s) | | (2bx+9x+4a)-(4bx-a)+(3b+a)= | | 6(3x-5)=3(6x+6) | | -2(q-4)=3q+12 | | 8(3a+7c)-6(2a+6c)= | | (2a^2b+7ab^2)+(3ab^2-2a^2b)= | | 8+2s-7=7s+3-4s | | -(3y+1)-(-2y-4)=-1 | | 3(x-2)(x+1)=0 | | -2y+6=20 | | 4z-7=5(5z-3) | | (5b-1)(6b-3)= | | 2x+20=304 | | -6x-(9y+(5x-(-2y-b))-(2b+a))= | | 2t^2-20t=0 | | 2(3v-1)+7v+7=5(v-6)+3v | | 304=s+20 | | 304=s+20w | | (4+w)(5w-8)=0 | | 30+9y=16y | | 5(w+2)-6(w+4)=0 | | (-6x-z)-(3y+(7x-(3z+8y+x)))= | | (5w+6)(5w-6)= | | -X+2x^2=0 | | -(8y+2)-(-7y-5)=-1 | | B=b+2a+3c | | 8(3x-8)=2(12x+7) | | (18y^2-12xy)-(6y^2+xy-a)= | | 3+3s-2=8s+5-3s |

Equations solver categories