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Simplifying 4x2 + 16x + -108 = 0 Reorder the terms: -108 + 16x + 4x2 = 0 Solving -108 + 16x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + 4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-27 + 4x + x2)' equal to zero and attempt to solve: Simplifying -27 + 4x + x2 = 0 Solving -27 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 4x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 4x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 4x + x2 = 0 + 27 4x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 4x + x2 = 27 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 = 27 + 4 Reorder the terms: 4 + 4x + x2 = 27 + 4 Combine like terms: 27 + 4 = 31 4 + 4x + x2 = 31 Factor a perfect square on the left side: (x + 2)(x + 2) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 2) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 2 = 5.567764363 Simplifying x + 2 = 5.567764363 Reorder the terms: 2 + x = 5.567764363 Solving 2 + x = 5.567764363 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 = 5.567764363 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.567764363 + -2 x = 5.567764363 + -2 Combine like terms: 5.567764363 + -2 = 3.567764363 x = 3.567764363 Simplifying x = 3.567764363Subproblem 2
x + 2 = -5.567764363 Simplifying x + 2 = -5.567764363 Reorder the terms: 2 + x = -5.567764363 Solving 2 + x = -5.567764363 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 = -5.567764363 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.567764363 + -2 x = -5.567764363 + -2 Combine like terms: -5.567764363 + -2 = -7.567764363 x = -7.567764363 Simplifying x = -7.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.567764363, -7.567764363}Solution
x = {3.567764363, -7.567764363}
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