-5(x^2-4)+7=2x+9

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Solution for -5(x^2-4)+7=2x+9 equation:


Simplifying
-5(x2 + -4) + 7 = 2x + 9

Reorder the terms:
-5(-4 + x2) + 7 = 2x + 9
(-4 * -5 + x2 * -5) + 7 = 2x + 9
(20 + -5x2) + 7 = 2x + 9

Reorder the terms:
20 + 7 + -5x2 = 2x + 9

Combine like terms: 20 + 7 = 27
27 + -5x2 = 2x + 9

Reorder the terms:
27 + -5x2 = 9 + 2x

Solving
27 + -5x2 = 9 + 2x

Solving for variable 'x'.

Reorder the terms:
27 + -9 + -2x + -5x2 = 9 + 2x + -9 + -2x

Combine like terms: 27 + -9 = 18
18 + -2x + -5x2 = 9 + 2x + -9 + -2x

Reorder the terms:
18 + -2x + -5x2 = 9 + -9 + 2x + -2x

Combine like terms: 9 + -9 = 0
18 + -2x + -5x2 = 0 + 2x + -2x
18 + -2x + -5x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
18 + -2x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-3.6 + 0.4x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 0.4x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 0.4x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 0.4x + x2 = 0 + 3.6
0.4x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
0.4x + x2 = 3.6

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 3.6 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 3.6 + 0.04

Combine like terms: 3.6 + 0.04 = 3.64
0.04 + 0.4x + x2 = 3.64

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 3.64

Calculate the square root of the right side: 1.907878403

Break this problem into two subproblems by setting 
(x + 0.2) equal to 1.907878403 and -1.907878403.

Subproblem 1

x + 0.2 = 1.907878403 Simplifying x + 0.2 = 1.907878403 Reorder the terms: 0.2 + x = 1.907878403 Solving 0.2 + x = 1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.907878403 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.907878403 + -0.2 x = 1.907878403 + -0.2 Combine like terms: 1.907878403 + -0.2 = 1.707878403 x = 1.707878403 Simplifying x = 1.707878403

Subproblem 2

x + 0.2 = -1.907878403 Simplifying x + 0.2 = -1.907878403 Reorder the terms: 0.2 + x = -1.907878403 Solving 0.2 + x = -1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.907878403 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.907878403 + -0.2 x = -1.907878403 + -0.2 Combine like terms: -1.907878403 + -0.2 = -2.107878403 x = -2.107878403 Simplifying x = -2.107878403

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.707878403, -2.107878403}

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