791=24x^2-7x

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Solution for 791=24x^2-7x equation:


Simplifying
791 = 24x2 + -7x

Reorder the terms:
791 = -7x + 24x2

Solving
791 = -7x + 24x2

Solving for variable 'x'.

Reorder the terms:
791 + 7x + -24x2 = -7x + 7x + 24x2 + -24x2

Combine like terms: -7x + 7x = 0
791 + 7x + -24x2 = 0 + 24x2 + -24x2
791 + 7x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
791 + 7x + -24x2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
-32.95833333 + -0.2916666667x + x2 = 0

Move the constant term to the right:

Add '32.95833333' to each side of the equation.
-32.95833333 + -0.2916666667x + 32.95833333 + x2 = 0 + 32.95833333

Reorder the terms:
-32.95833333 + 32.95833333 + -0.2916666667x + x2 = 0 + 32.95833333

Combine like terms: -32.95833333 + 32.95833333 = 0.00000000
0.00000000 + -0.2916666667x + x2 = 0 + 32.95833333
-0.2916666667x + x2 = 0 + 32.95833333

Combine like terms: 0 + 32.95833333 = 32.95833333
-0.2916666667x + x2 = 32.95833333

The x term is -0.2916666667x.  Take half its coefficient (-0.1458333334).
Square it (0.02126736113) and add it to both sides.

Add '0.02126736113' to each side of the equation.
-0.2916666667x + 0.02126736113 + x2 = 32.95833333 + 0.02126736113

Reorder the terms:
0.02126736113 + -0.2916666667x + x2 = 32.95833333 + 0.02126736113

Combine like terms: 32.95833333 + 0.02126736113 = 32.97960069113
0.02126736113 + -0.2916666667x + x2 = 32.97960069113

Factor a perfect square on the left side:
(x + -0.1458333334)(x + -0.1458333334) = 32.97960069113

Calculate the square root of the right side: 5.74278684

Break this problem into two subproblems by setting 
(x + -0.1458333334) equal to 5.74278684 and -5.74278684.

Subproblem 1

x + -0.1458333334 = 5.74278684 Simplifying x + -0.1458333334 = 5.74278684 Reorder the terms: -0.1458333334 + x = 5.74278684 Solving -0.1458333334 + x = 5.74278684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1458333334' to each side of the equation. -0.1458333334 + 0.1458333334 + x = 5.74278684 + 0.1458333334 Combine like terms: -0.1458333334 + 0.1458333334 = 0.0000000000 0.0000000000 + x = 5.74278684 + 0.1458333334 x = 5.74278684 + 0.1458333334 Combine like terms: 5.74278684 + 0.1458333334 = 5.8886201734 x = 5.8886201734 Simplifying x = 5.8886201734

Subproblem 2

x + -0.1458333334 = -5.74278684 Simplifying x + -0.1458333334 = -5.74278684 Reorder the terms: -0.1458333334 + x = -5.74278684 Solving -0.1458333334 + x = -5.74278684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1458333334' to each side of the equation. -0.1458333334 + 0.1458333334 + x = -5.74278684 + 0.1458333334 Combine like terms: -0.1458333334 + 0.1458333334 = 0.0000000000 0.0000000000 + x = -5.74278684 + 0.1458333334 x = -5.74278684 + 0.1458333334 Combine like terms: -5.74278684 + 0.1458333334 = -5.5969535066 x = -5.5969535066 Simplifying x = -5.5969535066

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.8886201734, -5.5969535066}

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