(x-3)(x+3)+10=4x

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Solution for (x-3)(x+3)+10=4x equation:


Simplifying
(x + -3)(x + 3) + 10 = 4x

Reorder the terms:
(-3 + x)(x + 3) + 10 = 4x

Reorder the terms:
(-3 + x)(3 + x) + 10 = 4x

Multiply (-3 + x) * (3 + x)
(-3(3 + x) + x(3 + x)) + 10 = 4x
((3 * -3 + x * -3) + x(3 + x)) + 10 = 4x
((-9 + -3x) + x(3 + x)) + 10 = 4x
(-9 + -3x + (3 * x + x * x)) + 10 = 4x
(-9 + -3x + (3x + x2)) + 10 = 4x

Combine like terms: -3x + 3x = 0
(-9 + 0 + x2) + 10 = 4x
(-9 + x2) + 10 = 4x

Reorder the terms:
-9 + 10 + x2 = 4x

Combine like terms: -9 + 10 = 1
1 + x2 = 4x

Solving
1 + x2 = 4x

Solving for variable 'x'.

Reorder the terms:
1 + -4x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
1 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -4x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x + x2 = 0 + -1
-4x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4x + x2 = -1

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1 + 4

Reorder the terms:
4 + -4x + x2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + -4x + x2 = 3

Factor a perfect square on the left side:
(x + -2)(x + -2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -2) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + -2 = 1.732050808 Simplifying x + -2 = 1.732050808 Reorder the terms: -2 + x = 1.732050808 Solving -2 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.732050808 + 2 x = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 x = 3.732050808 Simplifying x = 3.732050808

Subproblem 2

x + -2 = -1.732050808 Simplifying x + -2 = -1.732050808 Reorder the terms: -2 + x = -1.732050808 Solving -2 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.732050808 + 2 x = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 x = 0.267949192 Simplifying x = 0.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.732050808, 0.267949192}

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