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Simplifying x3 + 30x2 = -40x Reorder the terms: 30x2 + x3 = -40x Solving 30x2 + x3 = -40x Solving for variable 'x'. Reorder the terms: 40x + 30x2 + x3 = -40x + 40x Combine like terms: -40x + 40x = 0 40x + 30x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(40 + 30x + 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 '(40 + 30x + x2)' equal to zero and attempt to solve: Simplifying 40 + 30x + x2 = 0 Solving 40 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 30x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 30x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 30x + x2 = 0 + -40 30x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 30x + x2 = -40 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -40 + 225 Reorder the terms: 225 + 30x + x2 = -40 + 225 Combine like terms: -40 + 225 = 185 225 + 30x + x2 = 185 Factor a perfect square on the left side: (x + 15)(x + 15) = 185 Calculate the square root of the right side: 13.601470509 Break this problem into two subproblems by setting (x + 15) equal to 13.601470509 and -13.601470509.Subproblem 1
x + 15 = 13.601470509 Simplifying x + 15 = 13.601470509 Reorder the terms: 15 + x = 13.601470509 Solving 15 + x = 13.601470509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 13.601470509 + -15 Combine like terms: 15 + -15 = 0 0 + x = 13.601470509 + -15 x = 13.601470509 + -15 Combine like terms: 13.601470509 + -15 = -1.398529491 x = -1.398529491 Simplifying x = -1.398529491Subproblem 2
x + 15 = -13.601470509 Simplifying x + 15 = -13.601470509 Reorder the terms: 15 + x = -13.601470509 Solving 15 + x = -13.601470509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -13.601470509 + -15 Combine like terms: 15 + -15 = 0 0 + x = -13.601470509 + -15 x = -13.601470509 + -15 Combine like terms: -13.601470509 + -15 = -28.601470509 x = -28.601470509 Simplifying x = -28.601470509Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.398529491, -28.601470509}Solution
x = {0, -1.398529491, -28.601470509}
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