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Simplifying 10x3 + -4x2 + -18x = 0 Reorder the terms: -18x + -4x2 + 10x3 = 0 Solving -18x + -4x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-9 + -2x + 5x2) = 0 Ignore the factor 2.Subproblem 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 '(-9 + -2x + 5x2)' equal to zero and attempt to solve: Simplifying -9 + -2x + 5x2 = 0 Solving -9 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -0.4x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -0.4x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -0.4x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -0.4x + x2 = 0 + 1.8 -0.4x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -0.4x + x2 = 1.8 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 1.8 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 1.8 + 0.04 Combine like terms: 1.8 + 0.04 = 1.84 0.04 + -0.4x + x2 = 1.84 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + -0.2) equal to 1.356465997 and -1.356465997.Subproblem 1
x + -0.2 = 1.356465997 Simplifying x + -0.2 = 1.356465997 Reorder the terms: -0.2 + x = 1.356465997 Solving -0.2 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.356465997 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.356465997 + 0.2 x = 1.356465997 + 0.2 Combine like terms: 1.356465997 + 0.2 = 1.556465997 x = 1.556465997 Simplifying x = 1.556465997Subproblem 2
x + -0.2 = -1.356465997 Simplifying x + -0.2 = -1.356465997 Reorder the terms: -0.2 + x = -1.356465997 Solving -0.2 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.356465997 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.356465997 + 0.2 x = -1.356465997 + 0.2 Combine like terms: -1.356465997 + 0.2 = -1.156465997 x = -1.156465997 Simplifying x = -1.156465997Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.556465997, -1.156465997}Solution
x = {0, 1.556465997, -1.156465997}
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