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Simplifying 4x2 + 64x + 24 = 0 Reorder the terms: 24 + 64x + 4x2 = 0 Solving 24 + 64x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + 16x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + 16x + x2)' equal to zero and attempt to solve: Simplifying 6 + 16x + x2 = 0 Solving 6 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 16x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 16x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 16x + x2 = 0 + -6 16x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 16x + x2 = -6 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -6 + 64 Reorder the terms: 64 + 16x + x2 = -6 + 64 Combine like terms: -6 + 64 = 58 64 + 16x + x2 = 58 Factor a perfect square on the left side: (x + 8)(x + 8) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + 8) equal to 7.615773106 and -7.615773106.Subproblem 1
x + 8 = 7.615773106 Simplifying x + 8 = 7.615773106 Reorder the terms: 8 + x = 7.615773106 Solving 8 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 7.615773106 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.615773106 + -8 x = 7.615773106 + -8 Combine like terms: 7.615773106 + -8 = -0.384226894 x = -0.384226894 Simplifying x = -0.384226894Subproblem 2
x + 8 = -7.615773106 Simplifying x + 8 = -7.615773106 Reorder the terms: 8 + x = -7.615773106 Solving 8 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -7.615773106 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.615773106 + -8 x = -7.615773106 + -8 Combine like terms: -7.615773106 + -8 = -15.615773106 x = -15.615773106 Simplifying x = -15.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.384226894, -15.615773106}Solution
x = {-0.384226894, -15.615773106}
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