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Simplifying 2x3 + 21x2 = 40x Reorder the terms: 21x2 + 2x3 = 40x Solving 21x2 + 2x3 = 40x Solving for variable 'x'. Reorder the terms: -40x + 21x2 + 2x3 = 40x + -40x Combine like terms: 40x + -40x = 0 -40x + 21x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-40 + 21x + 2x2) = 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 + 21x + 2x2)' equal to zero and attempt to solve: Simplifying -40 + 21x + 2x2 = 0 Solving -40 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20 + 10.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 10.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 10.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 10.5x + x2 = 0 + 20 10.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 10.5x + x2 = 20 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 20 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 20 + 27.5625 Combine like terms: 20 + 27.5625 = 47.5625 27.5625 + 10.5x + x2 = 47.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 47.5625 Calculate the square root of the right side: 6.896557112 Break this problem into two subproblems by setting (x + 5.25) equal to 6.896557112 and -6.896557112.Subproblem 1
x + 5.25 = 6.896557112 Simplifying x + 5.25 = 6.896557112 Reorder the terms: 5.25 + x = 6.896557112 Solving 5.25 + x = 6.896557112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 6.896557112 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 6.896557112 + -5.25 x = 6.896557112 + -5.25 Combine like terms: 6.896557112 + -5.25 = 1.646557112 x = 1.646557112 Simplifying x = 1.646557112Subproblem 2
x + 5.25 = -6.896557112 Simplifying x + 5.25 = -6.896557112 Reorder the terms: 5.25 + x = -6.896557112 Solving 5.25 + x = -6.896557112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -6.896557112 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -6.896557112 + -5.25 x = -6.896557112 + -5.25 Combine like terms: -6.896557112 + -5.25 = -12.146557112 x = -12.146557112 Simplifying x = -12.146557112Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.646557112, -12.146557112}Solution
x = {0, 1.646557112, -12.146557112}
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