29x^2+25=70x

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Solution for 29x^2+25=70x equation:


Simplifying
29x2 + 25 = 70x

Reorder the terms:
25 + 29x2 = 70x

Solving
25 + 29x2 = 70x

Solving for variable 'x'.

Reorder the terms:
25 + -70x + 29x2 = 70x + -70x

Combine like terms: 70x + -70x = 0
25 + -70x + 29x2 = 0

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

Divide each side by '29'.
0.8620689655 + -2.413793103x + x2 = 0

Move the constant term to the right:

Add '-0.8620689655' to each side of the equation.
0.8620689655 + -2.413793103x + -0.8620689655 + x2 = 0 + -0.8620689655

Reorder the terms:
0.8620689655 + -0.8620689655 + -2.413793103x + x2 = 0 + -0.8620689655

Combine like terms: 0.8620689655 + -0.8620689655 = 0.0000000000
0.0000000000 + -2.413793103x + x2 = 0 + -0.8620689655
-2.413793103x + x2 = 0 + -0.8620689655

Combine like terms: 0 + -0.8620689655 = -0.8620689655
-2.413793103x + x2 = -0.8620689655

The x term is -2.413793103x.  Take half its coefficient (-1.206896552).
Square it (1.456599287) and add it to both sides.

Add '1.456599287' to each side of the equation.
-2.413793103x + 1.456599287 + x2 = -0.8620689655 + 1.456599287

Reorder the terms:
1.456599287 + -2.413793103x + x2 = -0.8620689655 + 1.456599287

Combine like terms: -0.8620689655 + 1.456599287 = 0.5945303215
1.456599287 + -2.413793103x + x2 = 0.5945303215

Factor a perfect square on the left side:
(x + -1.206896552)(x + -1.206896552) = 0.5945303215

Calculate the square root of the right side: 0.771057924

Break this problem into two subproblems by setting 
(x + -1.206896552) equal to 0.771057924 and -0.771057924.

Subproblem 1

x + -1.206896552 = 0.771057924 Simplifying x + -1.206896552 = 0.771057924 Reorder the terms: -1.206896552 + x = 0.771057924 Solving -1.206896552 + x = 0.771057924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.206896552' to each side of the equation. -1.206896552 + 1.206896552 + x = 0.771057924 + 1.206896552 Combine like terms: -1.206896552 + 1.206896552 = 0.000000000 0.000000000 + x = 0.771057924 + 1.206896552 x = 0.771057924 + 1.206896552 Combine like terms: 0.771057924 + 1.206896552 = 1.977954476 x = 1.977954476 Simplifying x = 1.977954476

Subproblem 2

x + -1.206896552 = -0.771057924 Simplifying x + -1.206896552 = -0.771057924 Reorder the terms: -1.206896552 + x = -0.771057924 Solving -1.206896552 + x = -0.771057924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.206896552' to each side of the equation. -1.206896552 + 1.206896552 + x = -0.771057924 + 1.206896552 Combine like terms: -1.206896552 + 1.206896552 = 0.000000000 0.000000000 + x = -0.771057924 + 1.206896552 x = -0.771057924 + 1.206896552 Combine like terms: -0.771057924 + 1.206896552 = 0.435838628 x = 0.435838628 Simplifying x = 0.435838628

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.977954476, 0.435838628}

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