4x^2-1=5x+3

Simple and best practice solution for 4x^2-1=5x+3 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 4x^2-1=5x+3 equation:


Simplifying
4x2 + -1 = 5x + 3

Reorder the terms:
-1 + 4x2 = 5x + 3

Reorder the terms:
-1 + 4x2 = 3 + 5x

Solving
-1 + 4x2 = 3 + 5x

Solving for variable 'x'.

Reorder the terms:
-1 + -3 + -5x + 4x2 = 3 + 5x + -3 + -5x

Combine like terms: -1 + -3 = -4
-4 + -5x + 4x2 = 3 + 5x + -3 + -5x

Reorder the terms:
-4 + -5x + 4x2 = 3 + -3 + 5x + -5x

Combine like terms: 3 + -3 = 0
-4 + -5x + 4x2 = 0 + 5x + -5x
-4 + -5x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-4 + -5x + 4x2 = 0

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

Divide each side by '4'.
-1 + -1.25x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.25x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.25x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.25x + x2 = 0 + 1
-1.25x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.25x + x2 = 1

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 1 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 1 + 0.390625

Combine like terms: 1 + 0.390625 = 1.390625
0.390625 + -1.25x + x2 = 1.390625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(x + -0.625) equal to 1.179247642 and -1.179247642.

Subproblem 1

x + -0.625 = 1.179247642 Simplifying x + -0.625 = 1.179247642 Reorder the terms: -0.625 + x = 1.179247642 Solving -0.625 + x = 1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.179247642 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.179247642 + 0.625 x = 1.179247642 + 0.625 Combine like terms: 1.179247642 + 0.625 = 1.804247642 x = 1.804247642 Simplifying x = 1.804247642

Subproblem 2

x + -0.625 = -1.179247642 Simplifying x + -0.625 = -1.179247642 Reorder the terms: -0.625 + x = -1.179247642 Solving -0.625 + x = -1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.179247642 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.179247642 + 0.625 x = -1.179247642 + 0.625 Combine like terms: -1.179247642 + 0.625 = -0.554247642 x = -0.554247642 Simplifying x = -0.554247642

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.804247642, -0.554247642}

See similar equations:

| 10x+(-6)=10 | | z+12=27 | | (y-2x)(y+2x)=20 | | s=8-7t | | 1-7v+6=-14 | | 3r+1=4 | | 1/3-5i | | b/19-9b/19=16/19 | | x-4-3x=-4 | | x+3.5+2x=13-4x | | 5z+2=4y | | 5/8X=14/5/8 | | 2(y-5/2)=.3 | | 10n=-80 | | 0.5r+0.25(t+16)=-6p+12 | | (tg^2x-3)(sen^2x-1)=0 | | 12y=228 | | 8t+17=23 | | b/13-7b/13=24/13 | | 8t+17=33 | | .6x-4=8 | | -5p=-55 | | h-2.5=-26.5 | | -8=x-3-2x | | -12x+16=-16x+11 | | (4x+3)(x-7)=0 | | (3x-6)(4x-3)=0 | | -3(-7p+2)=-174 | | -12x+16=16x+11 | | V+15=33 | | b/13-6b/13=15/13 | | -12x+16=13x+11 |

Equations solver categories