7x^2+29x-24=0

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Solution for 7x^2+29x-24=0 equation:


Simplifying
7x2 + 29x + -24 = 0

Reorder the terms:
-24 + 29x + 7x2 = 0

Solving
-24 + 29x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-3.428571429 + 4.142857143x + x2 = 0

Move the constant term to the right:

Add '3.428571429' to each side of the equation.
-3.428571429 + 4.142857143x + 3.428571429 + x2 = 0 + 3.428571429

Reorder the terms:
-3.428571429 + 3.428571429 + 4.142857143x + x2 = 0 + 3.428571429

Combine like terms: -3.428571429 + 3.428571429 = 0.000000000
0.000000000 + 4.142857143x + x2 = 0 + 3.428571429
4.142857143x + x2 = 0 + 3.428571429

Combine like terms: 0 + 3.428571429 = 3.428571429
4.142857143x + x2 = 3.428571429

The x term is 4.142857143x.  Take half its coefficient (2.071428572).
Square it (4.290816329) and add it to both sides.

Add '4.290816329' to each side of the equation.
4.142857143x + 4.290816329 + x2 = 3.428571429 + 4.290816329

Reorder the terms:
4.290816329 + 4.142857143x + x2 = 3.428571429 + 4.290816329

Combine like terms: 3.428571429 + 4.290816329 = 7.719387758
4.290816329 + 4.142857143x + x2 = 7.719387758

Factor a perfect square on the left side:
(x + 2.071428572)(x + 2.071428572) = 7.719387758

Calculate the square root of the right side: 2.77837862

Break this problem into two subproblems by setting 
(x + 2.071428572) equal to 2.77837862 and -2.77837862.

Subproblem 1

x + 2.071428572 = 2.77837862 Simplifying x + 2.071428572 = 2.77837862 Reorder the terms: 2.071428572 + x = 2.77837862 Solving 2.071428572 + x = 2.77837862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + x = 2.77837862 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = 2.77837862 + -2.071428572 x = 2.77837862 + -2.071428572 Combine like terms: 2.77837862 + -2.071428572 = 0.706950048 x = 0.706950048 Simplifying x = 0.706950048

Subproblem 2

x + 2.071428572 = -2.77837862 Simplifying x + 2.071428572 = -2.77837862 Reorder the terms: 2.071428572 + x = -2.77837862 Solving 2.071428572 + x = -2.77837862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + x = -2.77837862 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = -2.77837862 + -2.071428572 x = -2.77837862 + -2.071428572 Combine like terms: -2.77837862 + -2.071428572 = -4.849807192 x = -4.849807192 Simplifying x = -4.849807192

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.706950048, -4.849807192}

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