14x+x^2=17*15

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Solution for 14x+x^2=17*15 equation:


Simplifying
14x + x2 = 17 * 15

Multiply 17 * 15
14x + x2 = 255

Solving
14x + x2 = 255

Solving for variable 'x'.

Reorder the terms:
-255 + 14x + x2 = 255 + -255

Combine like terms: 255 + -255 = 0
-255 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '255' to each side of the equation.
-255 + 14x + 255 + x2 = 0 + 255

Reorder the terms:
-255 + 255 + 14x + x2 = 0 + 255

Combine like terms: -255 + 255 = 0
0 + 14x + x2 = 0 + 255
14x + x2 = 0 + 255

Combine like terms: 0 + 255 = 255
14x + x2 = 255

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 255 + 49

Reorder the terms:
49 + 14x + x2 = 255 + 49

Combine like terms: 255 + 49 = 304
49 + 14x + x2 = 304

Factor a perfect square on the left side:
(x + 7)(x + 7) = 304

Calculate the square root of the right side: 17.435595774

Break this problem into two subproblems by setting 
(x + 7) equal to 17.435595774 and -17.435595774.

Subproblem 1

x + 7 = 17.435595774 Simplifying x + 7 = 17.435595774 Reorder the terms: 7 + x = 17.435595774 Solving 7 + x = 17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 17.435595774 + -7 Combine like terms: 7 + -7 = 0 0 + x = 17.435595774 + -7 x = 17.435595774 + -7 Combine like terms: 17.435595774 + -7 = 10.435595774 x = 10.435595774 Simplifying x = 10.435595774

Subproblem 2

x + 7 = -17.435595774 Simplifying x + 7 = -17.435595774 Reorder the terms: 7 + x = -17.435595774 Solving 7 + x = -17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -17.435595774 + -7 Combine like terms: 7 + -7 = 0 0 + x = -17.435595774 + -7 x = -17.435595774 + -7 Combine like terms: -17.435595774 + -7 = -24.435595774 x = -24.435595774 Simplifying x = -24.435595774

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.435595774, -24.435595774}

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