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Simplifying -2x(x2 + 5x + -9) = 0 Reorder the terms: -2x(-9 + 5x + x2) = 0 (-9 * -2x + 5x * -2x + x2 * -2x) = 0 (18x + -10x2 + -2x3) = 0 Solving 18x + -10x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(9 + -5x + -1x2) = 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 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 9 + -5x + -1x2 = 0 Solving 9 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5x + x2 = 0 + 9 5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 5x + x2 = 9 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 9 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 9 + 6.25 Combine like terms: 9 + 6.25 = 15.25 6.25 + 5x + x2 = 15.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 2.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 2.5 = 3.905124838 Simplifying x + 2.5 = 3.905124838 Reorder the terms: 2.5 + x = 3.905124838 Solving 2.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.905124838 + -2.5 x = 3.905124838 + -2.5 Combine like terms: 3.905124838 + -2.5 = 1.405124838 x = 1.405124838 Simplifying x = 1.405124838Subproblem 2
x + 2.5 = -3.905124838 Simplifying x + 2.5 = -3.905124838 Reorder the terms: 2.5 + x = -3.905124838 Solving 2.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.905124838 + -2.5 x = -3.905124838 + -2.5 Combine like terms: -3.905124838 + -2.5 = -6.405124838 x = -6.405124838 Simplifying x = -6.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.405124838, -6.405124838}Solution
x = {0, 1.405124838, -6.405124838}
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