4x^2-29x+48=0

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Solution for 4x^2-29x+48=0 equation:


Simplifying
4x2 + -29x + 48 = 0

Reorder the terms:
48 + -29x + 4x2 = 0

Solving
48 + -29x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
12 + -7.25x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -7.25x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -7.25x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -7.25x + x2 = 0 + -12
-7.25x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-7.25x + x2 = -12

The x term is -7.25x.  Take half its coefficient (-3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
-7.25x + 13.140625 + x2 = -12 + 13.140625

Reorder the terms:
13.140625 + -7.25x + x2 = -12 + 13.140625

Combine like terms: -12 + 13.140625 = 1.140625
13.140625 + -7.25x + x2 = 1.140625

Factor a perfect square on the left side:
(x + -3.625)(x + -3.625) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + -3.625) equal to 1.068000468 and -1.068000468.

Subproblem 1

x + -3.625 = 1.068000468 Simplifying x + -3.625 = 1.068000468 Reorder the terms: -3.625 + x = 1.068000468 Solving -3.625 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 1.068000468 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 1.068000468 + 3.625 x = 1.068000468 + 3.625 Combine like terms: 1.068000468 + 3.625 = 4.693000468 x = 4.693000468 Simplifying x = 4.693000468

Subproblem 2

x + -3.625 = -1.068000468 Simplifying x + -3.625 = -1.068000468 Reorder the terms: -3.625 + x = -1.068000468 Solving -3.625 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -1.068000468 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -1.068000468 + 3.625 x = -1.068000468 + 3.625 Combine like terms: -1.068000468 + 3.625 = 2.556999532 x = 2.556999532 Simplifying x = 2.556999532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.693000468, 2.556999532}

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