7x^2-15+38x=0

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Solution for 7x^2-15+38x=0 equation:


Simplifying
7x2 + -15 + 38x = 0

Reorder the terms:
-15 + 38x + 7x2 = 0

Solving
-15 + 38x + 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'.
-2.142857143 + 5.428571429x + x2 = 0

Move the constant term to the right:

Add '2.142857143' to each side of the equation.
-2.142857143 + 5.428571429x + 2.142857143 + x2 = 0 + 2.142857143

Reorder the terms:
-2.142857143 + 2.142857143 + 5.428571429x + x2 = 0 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + 5.428571429x + x2 = 0 + 2.142857143
5.428571429x + x2 = 0 + 2.142857143

Combine like terms: 0 + 2.142857143 = 2.142857143
5.428571429x + x2 = 2.142857143

The x term is 5.428571429x.  Take half its coefficient (2.714285715).
Square it (7.367346943) and add it to both sides.

Add '7.367346943' to each side of the equation.
5.428571429x + 7.367346943 + x2 = 2.142857143 + 7.367346943

Reorder the terms:
7.367346943 + 5.428571429x + x2 = 2.142857143 + 7.367346943

Combine like terms: 2.142857143 + 7.367346943 = 9.510204086
7.367346943 + 5.428571429x + x2 = 9.510204086

Factor a perfect square on the left side:
(x + 2.714285715)(x + 2.714285715) = 9.510204086

Calculate the square root of the right side: 3.083861879

Break this problem into two subproblems by setting 
(x + 2.714285715) equal to 3.083861879 and -3.083861879.

Subproblem 1

x + 2.714285715 = 3.083861879 Simplifying x + 2.714285715 = 3.083861879 Reorder the terms: 2.714285715 + x = 3.083861879 Solving 2.714285715 + x = 3.083861879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.714285715' to each side of the equation. 2.714285715 + -2.714285715 + x = 3.083861879 + -2.714285715 Combine like terms: 2.714285715 + -2.714285715 = 0.000000000 0.000000000 + x = 3.083861879 + -2.714285715 x = 3.083861879 + -2.714285715 Combine like terms: 3.083861879 + -2.714285715 = 0.369576164 x = 0.369576164 Simplifying x = 0.369576164

Subproblem 2

x + 2.714285715 = -3.083861879 Simplifying x + 2.714285715 = -3.083861879 Reorder the terms: 2.714285715 + x = -3.083861879 Solving 2.714285715 + x = -3.083861879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.714285715' to each side of the equation. 2.714285715 + -2.714285715 + x = -3.083861879 + -2.714285715 Combine like terms: 2.714285715 + -2.714285715 = 0.000000000 0.000000000 + x = -3.083861879 + -2.714285715 x = -3.083861879 + -2.714285715 Combine like terms: -3.083861879 + -2.714285715 = -5.798147594 x = -5.798147594 Simplifying x = -5.798147594

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.369576164, -5.798147594}

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