4X^2=3X+3

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Solution for 4X^2=3X+3 equation:


Simplifying
4X2 = 3X + 3

Reorder the terms:
4X2 = 3 + 3X

Solving
4X2 = 3 + 3X

Solving for variable 'X'.

Reorder the terms:
-3 + -3X + 4X2 = 3 + 3X + -3 + -3X

Reorder the terms:
-3 + -3X + 4X2 = 3 + -3 + 3X + -3X

Combine like terms: 3 + -3 = 0
-3 + -3X + 4X2 = 0 + 3X + -3X
-3 + -3X + 4X2 = 3X + -3X

Combine like terms: 3X + -3X = 0
-3 + -3X + 4X2 = 0

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

Divide each side by '4'.
-0.75 + -0.75X + X2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.75X + 0.75 + X2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.75X + X2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.75X + X2 = 0 + 0.75
-0.75X + X2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.75X + X2 = 0.75

The X term is -0.75X.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75X + 0.140625 + X2 = 0.75 + 0.140625

Reorder the terms:
0.140625 + -0.75X + X2 = 0.75 + 0.140625

Combine like terms: 0.75 + 0.140625 = 0.890625
0.140625 + -0.75X + X2 = 0.890625

Factor a perfect square on the left side:
(X + -0.375)(X + -0.375) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(X + -0.375) equal to 0.943729304 and -0.943729304.

Subproblem 1

X + -0.375 = 0.943729304 Simplifying X + -0.375 = 0.943729304 Reorder the terms: -0.375 + X = 0.943729304 Solving -0.375 + X = 0.943729304 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + X = 0.943729304 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + X = 0.943729304 + 0.375 X = 0.943729304 + 0.375 Combine like terms: 0.943729304 + 0.375 = 1.318729304 X = 1.318729304 Simplifying X = 1.318729304

Subproblem 2

X + -0.375 = -0.943729304 Simplifying X + -0.375 = -0.943729304 Reorder the terms: -0.375 + X = -0.943729304 Solving -0.375 + X = -0.943729304 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + X = -0.943729304 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + X = -0.943729304 + 0.375 X = -0.943729304 + 0.375 Combine like terms: -0.943729304 + 0.375 = -0.568729304 X = -0.568729304 Simplifying X = -0.568729304

Solution

The solution to the problem is based on the solutions from the subproblems. X = {1.318729304, -0.568729304}

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