2x^2+7x-29=0

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


Simplifying
2x2 + 7x + -29 = 0

Reorder the terms:
-29 + 7x + 2x2 = 0

Solving
-29 + 7x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-14.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '14.5' to each side of the equation.
-14.5 + 3.5x + 14.5 + x2 = 0 + 14.5

Reorder the terms:
-14.5 + 14.5 + 3.5x + x2 = 0 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + 3.5x + x2 = 0 + 14.5
3.5x + x2 = 0 + 14.5

Combine like terms: 0 + 14.5 = 14.5
3.5x + x2 = 14.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 14.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 14.5 + 3.0625

Combine like terms: 14.5 + 3.0625 = 17.5625
3.0625 + 3.5x + x2 = 17.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 17.5625

Calculate the square root of the right side: 4.190763654

Break this problem into two subproblems by setting 
(x + 1.75) equal to 4.190763654 and -4.190763654.

Subproblem 1

x + 1.75 = 4.190763654 Simplifying x + 1.75 = 4.190763654 Reorder the terms: 1.75 + x = 4.190763654 Solving 1.75 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.190763654 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.190763654 + -1.75 x = 4.190763654 + -1.75 Combine like terms: 4.190763654 + -1.75 = 2.440763654 x = 2.440763654 Simplifying x = 2.440763654

Subproblem 2

x + 1.75 = -4.190763654 Simplifying x + 1.75 = -4.190763654 Reorder the terms: 1.75 + x = -4.190763654 Solving 1.75 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.190763654 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.190763654 + -1.75 x = -4.190763654 + -1.75 Combine like terms: -4.190763654 + -1.75 = -5.940763654 x = -5.940763654 Simplifying x = -5.940763654

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.440763654, -5.940763654}

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