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Simplifying 10x3 + 230x2 + 120x = 0 Reorder the terms: 120x + 230x2 + 10x3 = 0 Solving 120x + 230x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x'. 10x(12 + 23x + x2) = 0 Ignore the factor 10.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 '(12 + 23x + x2)' equal to zero and attempt to solve: Simplifying 12 + 23x + x2 = 0 Solving 12 + 23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 23x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 23x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 23x + x2 = 0 + -12 23x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 23x + x2 = -12 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = -12 + 132.25 Reorder the terms: 132.25 + 23x + x2 = -12 + 132.25 Combine like terms: -12 + 132.25 = 120.25 132.25 + 23x + x2 = 120.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 11.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 11.5 = 10.9658561 Simplifying x + 11.5 = 10.9658561 Reorder the terms: 11.5 + x = 10.9658561 Solving 11.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 10.9658561 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 10.9658561 + -11.5 x = 10.9658561 + -11.5 Combine like terms: 10.9658561 + -11.5 = -0.5341439 x = -0.5341439 Simplifying x = -0.5341439Subproblem 2
x + 11.5 = -10.9658561 Simplifying x + 11.5 = -10.9658561 Reorder the terms: 11.5 + x = -10.9658561 Solving 11.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -10.9658561 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -10.9658561 + -11.5 x = -10.9658561 + -11.5 Combine like terms: -10.9658561 + -11.5 = -22.4658561 x = -22.4658561 Simplifying x = -22.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5341439, -22.4658561}Solution
x = {0, -0.5341439, -22.4658561}
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