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Simplifying 0 = x3 + 3x2 + -25x Reorder the terms: 0 = -25x + 3x2 + x3 Solving 0 = -25x + 3x2 + x3 Solving for variable 'x'. Remove the zero: 25x + -3x2 + -1x3 = -25x + 3x2 + x3 + 25x + -3x2 + -1x3 Reorder the terms: 25x + -3x2 + -1x3 = -25x + 25x + 3x2 + -3x2 + x3 + -1x3 Combine like terms: -25x + 25x = 0 25x + -3x2 + -1x3 = 0 + 3x2 + -3x2 + x3 + -1x3 25x + -3x2 + -1x3 = 3x2 + -3x2 + x3 + -1x3 Combine like terms: 3x2 + -3x2 = 0 25x + -3x2 + -1x3 = 0 + x3 + -1x3 25x + -3x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 25x + -3x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(25 + -3x + -1x2) = 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 '(25 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 25 + -3x + -1x2 = 0 Solving 25 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 3x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 3x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 3x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 3x + x2 = 0 + 25 3x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 3x + x2 = 25 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 = 25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 25 + 2.25 Combine like terms: 25 + 2.25 = 27.25 2.25 + 3x + x2 = 27.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 1.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 1.5 = 5.220153254 Simplifying x + 1.5 = 5.220153254 Reorder the terms: 1.5 + x = 5.220153254 Solving 1.5 + x = 5.220153254 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 = 5.220153254 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.220153254 + -1.5 x = 5.220153254 + -1.5 Combine like terms: 5.220153254 + -1.5 = 3.720153254 x = 3.720153254 Simplifying x = 3.720153254Subproblem 2
x + 1.5 = -5.220153254 Simplifying x + 1.5 = -5.220153254 Reorder the terms: 1.5 + x = -5.220153254 Solving 1.5 + x = -5.220153254 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 = -5.220153254 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.220153254 + -1.5 x = -5.220153254 + -1.5 Combine like terms: -5.220153254 + -1.5 = -6.720153254 x = -6.720153254 Simplifying x = -6.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.720153254, -6.720153254}Solution
x = {0, 3.720153254, -6.720153254}
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