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Simplifying (6x2 + -3x) + -1(3x2 + -8x3) = 0 Reorder the terms: (-3x + 6x2) + -1(3x2 + -8x3) = 0 Remove parenthesis around (-3x + 6x2) -3x + 6x2 + -1(3x2 + -8x3) = 0 -3x + 6x2 + (3x2 * -1 + -8x3 * -1) = 0 -3x + 6x2 + (-3x2 + 8x3) = 0 Combine like terms: 6x2 + -3x2 = 3x2 -3x + 3x2 + 8x3 = 0 Solving -3x + 3x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + 3x + 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 + 3x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + 3x + 8x2 = 0 Solving -3 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 0.375x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 0.375x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 0.375x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 0.375x + x2 = 0 + 0.375 0.375x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 0.375x + x2 = 0.375 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 0.375 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 0.375 + 0.03515625 Combine like terms: 0.375 + 0.03515625 = 0.41015625 0.03515625 + 0.375x + x2 = 0.41015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 0.41015625 Calculate the square root of the right side: 0.640434423 Break this problem into two subproblems by setting (x + 0.1875) equal to 0.640434423 and -0.640434423.Subproblem 1
x + 0.1875 = 0.640434423 Simplifying x + 0.1875 = 0.640434423 Reorder the terms: 0.1875 + x = 0.640434423 Solving 0.1875 + x = 0.640434423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 0.640434423 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 0.640434423 + -0.1875 x = 0.640434423 + -0.1875 Combine like terms: 0.640434423 + -0.1875 = 0.452934423 x = 0.452934423 Simplifying x = 0.452934423Subproblem 2
x + 0.1875 = -0.640434423 Simplifying x + 0.1875 = -0.640434423 Reorder the terms: 0.1875 + x = -0.640434423 Solving 0.1875 + x = -0.640434423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -0.640434423 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -0.640434423 + -0.1875 x = -0.640434423 + -0.1875 Combine like terms: -0.640434423 + -0.1875 = -0.827934423 x = -0.827934423 Simplifying x = -0.827934423Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.452934423, -0.827934423}Solution
x = {0, 0.452934423, -0.827934423}
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