4x(2x+6)=24

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Solution for 4x(2x+6)=24 equation:


Simplifying
4x(2x + 6) = 24

Reorder the terms:
4x(6 + 2x) = 24
(6 * 4x + 2x * 4x) = 24
(24x + 8x2) = 24

Solving
24x + 8x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 24x + 8x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 24x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-3 + 3x + x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(-3 + 3x + x2)' equal to zero and attempt to solve: Simplifying -3 + 3x + x2 = 0 Solving -3 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 3x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 3x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3x + x2 = 0 + 3 3x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 3x + x2 = 3 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 3 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + 3x + x2 = 5.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + 1.5 = 2.291287847 Simplifying x + 1.5 = 2.291287847 Reorder the terms: 1.5 + x = 2.291287847 Solving 1.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.291287847 + -1.5 x = 2.291287847 + -1.5 Combine like terms: 2.291287847 + -1.5 = 0.791287847 x = 0.791287847 Simplifying x = 0.791287847

Subproblem 2

x + 1.5 = -2.291287847 Simplifying x + 1.5 = -2.291287847 Reorder the terms: 1.5 + x = -2.291287847 Solving 1.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.291287847 + -1.5 x = -2.291287847 + -1.5 Combine like terms: -2.291287847 + -1.5 = -3.791287847 x = -3.791287847 Simplifying x = -3.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.791287847, -3.791287847}

Solution

x = {0.791287847, -3.791287847}

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