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Simplifying 8x3 + 17x2 + 3x = 0 Reorder the terms: 3x + 17x2 + 8x3 = 0 Solving 3x + 17x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 17x + 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 '(3 + 17x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 17x + 8x2 = 0 Solving 3 + 17x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 2.125x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 2.125x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 2.125x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 2.125x + x2 = 0 + -0.375 2.125x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 2.125x + x2 = -0.375 The x term is 2.125x. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125x + 1.12890625 + x2 = -0.375 + 1.12890625 Reorder the terms: 1.12890625 + 2.125x + x2 = -0.375 + 1.12890625 Combine like terms: -0.375 + 1.12890625 = 0.75390625 1.12890625 + 2.125x + x2 = 0.75390625 Factor a perfect square on the left side: (x + 1.0625)(x + 1.0625) = 0.75390625 Calculate the square root of the right side: 0.868277749 Break this problem into two subproblems by setting (x + 1.0625) equal to 0.868277749 and -0.868277749.Subproblem 1
x + 1.0625 = 0.868277749 Simplifying x + 1.0625 = 0.868277749 Reorder the terms: 1.0625 + x = 0.868277749 Solving 1.0625 + x = 0.868277749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = 0.868277749 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = 0.868277749 + -1.0625 x = 0.868277749 + -1.0625 Combine like terms: 0.868277749 + -1.0625 = -0.194222251 x = -0.194222251 Simplifying x = -0.194222251Subproblem 2
x + 1.0625 = -0.868277749 Simplifying x + 1.0625 = -0.868277749 Reorder the terms: 1.0625 + x = -0.868277749 Solving 1.0625 + x = -0.868277749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = -0.868277749 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = -0.868277749 + -1.0625 x = -0.868277749 + -1.0625 Combine like terms: -0.868277749 + -1.0625 = -1.930777749 x = -1.930777749 Simplifying x = -1.930777749Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.194222251, -1.930777749}Solution
x = {0, -0.194222251, -1.930777749}
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