4x^2-24x+7=0

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Solution for 4x^2-24x+7=0 equation:


Simplifying
4x2 + -24x + 7 = 0

Reorder the terms:
7 + -24x + 4x2 = 0

Solving
7 + -24x + 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'.
1.75 + -6x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -6x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -6x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -6x + x2 = 0 + -1.75
-6x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-6x + x2 = -1.75

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -1.75 + 9

Reorder the terms:
9 + -6x + x2 = -1.75 + 9

Combine like terms: -1.75 + 9 = 7.25
9 + -6x + x2 = 7.25

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + -3) equal to 2.692582404 and -2.692582404.

Subproblem 1

x + -3 = 2.692582404 Simplifying x + -3 = 2.692582404 Reorder the terms: -3 + x = 2.692582404 Solving -3 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.692582404 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.692582404 + 3 x = 2.692582404 + 3 Combine like terms: 2.692582404 + 3 = 5.692582404 x = 5.692582404 Simplifying x = 5.692582404

Subproblem 2

x + -3 = -2.692582404 Simplifying x + -3 = -2.692582404 Reorder the terms: -3 + x = -2.692582404 Solving -3 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.692582404 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.692582404 + 3 x = -2.692582404 + 3 Combine like terms: -2.692582404 + 3 = 0.307417596 x = 0.307417596 Simplifying x = 0.307417596

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.692582404, 0.307417596}

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