x^2=7x+15

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


Simplifying
x2 = 7x + 15

Reorder the terms:
x2 = 15 + 7x

Solving
x2 = 15 + 7x

Solving for variable 'x'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -7x + 15 + x2 = 0 + 15

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

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

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

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 15 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 15 + 12.25

Combine like terms: 15 + 12.25 = 27.25
12.25 + -7x + x2 = 27.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -3.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

x + -3.5 = 5.220153254 Simplifying x + -3.5 = 5.220153254 Reorder the terms: -3.5 + x = 5.220153254 Solving -3.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.220153254 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.220153254 + 3.5 x = 5.220153254 + 3.5 Combine like terms: 5.220153254 + 3.5 = 8.720153254 x = 8.720153254 Simplifying x = 8.720153254

Subproblem 2

x + -3.5 = -5.220153254 Simplifying x + -3.5 = -5.220153254 Reorder the terms: -3.5 + x = -5.220153254 Solving -3.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.220153254 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.220153254 + 3.5 x = -5.220153254 + 3.5 Combine like terms: -5.220153254 + 3.5 = -1.720153254 x = -1.720153254 Simplifying x = -1.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.720153254, -1.720153254}

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