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Simplifying 8x3 + 15x2 + 2x = 0 Reorder the terms: 2x + 15x2 + 8x3 = 0 Solving 2x + 15x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + 15x + 8x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(2 + 15x + 8x2)' equal to zero and attempt to solve: Simplifying 2 + 15x + 8x2 = 0 Solving 2 + 15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + 1.875x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.875x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.875x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.875x + x2 = 0 + -0.25 1.875x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.875x + x2 = -0.25 The x term is 1.875x. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875x + 0.87890625 + x2 = -0.25 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = -0.25 + 0.87890625 Combine like terms: -0.25 + 0.87890625 = 0.62890625 0.87890625 + 1.875x + x2 = 0.62890625 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = 0.62890625 Calculate the square root of the right side: 0.793036096 Break this problem into two subproblems by setting (x + 0.9375) equal to 0.793036096 and -0.793036096.Subproblem 1
x + 0.9375 = 0.793036096 Simplifying x + 0.9375 = 0.793036096 Reorder the terms: 0.9375 + x = 0.793036096 Solving 0.9375 + x = 0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = 0.793036096 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 0.793036096 + -0.9375 x = 0.793036096 + -0.9375 Combine like terms: 0.793036096 + -0.9375 = -0.144463904 x = -0.144463904 Simplifying x = -0.144463904Subproblem 2
x + 0.9375 = -0.793036096 Simplifying x + 0.9375 = -0.793036096 Reorder the terms: 0.9375 + x = -0.793036096 Solving 0.9375 + x = -0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = -0.793036096 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -0.793036096 + -0.9375 x = -0.793036096 + -0.9375 Combine like terms: -0.793036096 + -0.9375 = -1.730536096 x = -1.730536096 Simplifying x = -1.730536096Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.144463904, -1.730536096}Solution
x = {0, -0.144463904, -1.730536096}
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