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Simplifying x(x2 + -3x + -98) = 0 Reorder the terms: x(-98 + -3x + x2) = 0 (-98 * x + -3x * x + x2 * x) = 0 (-98x + -3x2 + x3) = 0 Solving -98x + -3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-98 + -3x + x2) = 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 '(-98 + -3x + x2)' equal to zero and attempt to solve: Simplifying -98 + -3x + x2 = 0 Solving -98 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -3x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -3x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -3x + x2 = 0 + 98 -3x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -3x + x2 = 98 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 98 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 98 + 2.25 Combine like terms: 98 + 2.25 = 100.25 2.25 + -3x + x2 = 100.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -1.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -1.5 = 10.012492197 Simplifying x + -1.5 = 10.012492197 Reorder the terms: -1.5 + x = 10.012492197 Solving -1.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 10.012492197 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.012492197 + 1.5 x = 10.012492197 + 1.5 Combine like terms: 10.012492197 + 1.5 = 11.512492197 x = 11.512492197 Simplifying x = 11.512492197Subproblem 2
x + -1.5 = -10.012492197 Simplifying x + -1.5 = -10.012492197 Reorder the terms: -1.5 + x = -10.012492197 Solving -1.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -10.012492197 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.012492197 + 1.5 x = -10.012492197 + 1.5 Combine like terms: -10.012492197 + 1.5 = -8.512492197 x = -8.512492197 Simplifying x = -8.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.512492197, -8.512492197}Solution
x = {0, 11.512492197, -8.512492197}
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