7x^2+15x=5

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Solution for 7x^2+15x=5 equation:


Simplifying
7x2 + 15x = 5

Reorder the terms:
15x + 7x2 = 5

Solving
15x + 7x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 15x + 7x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 15x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + 2.142857143x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 2.142857143x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 2.142857143x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 2.142857143x + x2 = 0 + 0.7142857143
2.142857143x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
2.142857143x + x2 = 0.7142857143

The x term is 2.142857143x.  Take half its coefficient (1.071428572).
Square it (1.147959185) and add it to both sides.

Add '1.147959185' to each side of the equation.
2.142857143x + 1.147959185 + x2 = 0.7142857143 + 1.147959185

Reorder the terms:
1.147959185 + 2.142857143x + x2 = 0.7142857143 + 1.147959185

Combine like terms: 0.7142857143 + 1.147959185 = 1.8622448993
1.147959185 + 2.142857143x + x2 = 1.8622448993

Factor a perfect square on the left side:
(x + 1.071428572)(x + 1.071428572) = 1.8622448993

Calculate the square root of the right side: 1.364640942

Break this problem into two subproblems by setting 
(x + 1.071428572) equal to 1.364640942 and -1.364640942.

Subproblem 1

x + 1.071428572 = 1.364640942 Simplifying x + 1.071428572 = 1.364640942 Reorder the terms: 1.071428572 + x = 1.364640942 Solving 1.071428572 + x = 1.364640942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = 1.364640942 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 1.364640942 + -1.071428572 x = 1.364640942 + -1.071428572 Combine like terms: 1.364640942 + -1.071428572 = 0.29321237 x = 0.29321237 Simplifying x = 0.29321237

Subproblem 2

x + 1.071428572 = -1.364640942 Simplifying x + 1.071428572 = -1.364640942 Reorder the terms: 1.071428572 + x = -1.364640942 Solving 1.071428572 + x = -1.364640942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = -1.364640942 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -1.364640942 + -1.071428572 x = -1.364640942 + -1.071428572 Combine like terms: -1.364640942 + -1.071428572 = -2.436069514 x = -2.436069514 Simplifying x = -2.436069514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.29321237, -2.436069514}

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