(x+1)(x-3)=10

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Solution for (x+1)(x-3)=10 equation:


Simplifying
(x + 1)(x + -3) = 10

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

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

Multiply (1 + x) * (-3 + x)
(1(-3 + x) + x(-3 + x)) = 10
((-3 * 1 + x * 1) + x(-3 + x)) = 10
((-3 + 1x) + x(-3 + x)) = 10
(-3 + 1x + (-3 * x + x * x)) = 10
(-3 + 1x + (-3x + x2)) = 10

Combine like terms: 1x + -3x = -2x
(-3 + -2x + x2) = 10

Solving
-3 + -2x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-3 + -10 + -2x + x2 = 10 + -10

Combine like terms: -3 + -10 = -13
-13 + -2x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-13 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -2x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -2x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x + x2 = 0 + 13
-2x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-2x + x2 = 13

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 13 + 1

Reorder the terms:
1 + -2x + x2 = 13 + 1

Combine like terms: 13 + 1 = 14
1 + -2x + x2 = 14

Factor a perfect square on the left side:
(x + -1)(x + -1) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -1) equal to 3.741657387 and -3.741657387.

Subproblem 1

x + -1 = 3.741657387 Simplifying x + -1 = 3.741657387 Reorder the terms: -1 + x = 3.741657387 Solving -1 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.741657387 + 1 x = 3.741657387 + 1 Combine like terms: 3.741657387 + 1 = 4.741657387 x = 4.741657387 Simplifying x = 4.741657387

Subproblem 2

x + -1 = -3.741657387 Simplifying x + -1 = -3.741657387 Reorder the terms: -1 + x = -3.741657387 Solving -1 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.741657387 + 1 x = -3.741657387 + 1 Combine like terms: -3.741657387 + 1 = -2.741657387 x = -2.741657387 Simplifying x = -2.741657387

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.741657387, -2.741657387}

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