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Simplifying 4x2 + 12x = 32 Reorder the terms: 12x + 4x2 = 32 Solving 12x + 4x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 12x + 4x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + 3x + x2)' equal to zero and attempt to solve: Simplifying -8 + 3x + x2 = 0 Solving -8 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 3x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 3x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3x + x2 = 0 + 8 3x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 3x + x2 = 8 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 = 8 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + 3x + x2 = 10.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + 1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + 1.5 = 3.201562119 Simplifying x + 1.5 = 3.201562119 Reorder the terms: 1.5 + x = 3.201562119 Solving 1.5 + x = 3.201562119 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 = 3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.201562119 + -1.5 x = 3.201562119 + -1.5 Combine like terms: 3.201562119 + -1.5 = 1.701562119 x = 1.701562119 Simplifying x = 1.701562119Subproblem 2
x + 1.5 = -3.201562119 Simplifying x + 1.5 = -3.201562119 Reorder the terms: 1.5 + x = -3.201562119 Solving 1.5 + x = -3.201562119 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 = -3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.201562119 + -1.5 x = -3.201562119 + -1.5 Combine like terms: -3.201562119 + -1.5 = -4.701562119 x = -4.701562119 Simplifying x = -4.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.701562119, -4.701562119}Solution
x = {1.701562119, -4.701562119}
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