2x^2+8x=32

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Solution for 2x^2+8x=32 equation:


Simplifying
2x2 + 8x = 32

Reorder the terms:
8x + 2x2 = 32

Solving
8x + 2x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + 8x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-16 + 4x + x2)' equal to zero and attempt to solve: Simplifying -16 + 4x + x2 = 0 Solving -16 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 4x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 4x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 4x + x2 = 0 + 16 4x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 4x + x2 = 16 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 = 16 + 4 Reorder the terms: 4 + 4x + x2 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + 4x + x2 = 20 Factor a perfect square on the left side: (x + 2)(x + 2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 2) equal to 4.472135955 and -4.472135955.

Subproblem 1

x + 2 = 4.472135955 Simplifying x + 2 = 4.472135955 Reorder the terms: 2 + x = 4.472135955 Solving 2 + x = 4.472135955 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 = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.472135955 + -2 x = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 x = 2.472135955 Simplifying x = 2.472135955

Subproblem 2

x + 2 = -4.472135955 Simplifying x + 2 = -4.472135955 Reorder the terms: 2 + x = -4.472135955 Solving 2 + x = -4.472135955 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 = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.472135955 + -2 x = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 x = -6.472135955 Simplifying x = -6.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.472135955, -6.472135955}

Solution

x = {2.472135955, -6.472135955}

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