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Simplifying 240x3 + 675x2 + -2160x = 0 Reorder the terms: -2160x + 675x2 + 240x3 = 0 Solving -2160x + 675x2 + 240x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15x'. 15x(-144 + 45x + 16x2) = 0 Ignore the factor 15.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 '(-144 + 45x + 16x2)' equal to zero and attempt to solve: Simplifying -144 + 45x + 16x2 = 0 Solving -144 + 45x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9 + 2.8125x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 2.8125x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 2.8125x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2.8125x + x2 = 0 + 9 2.8125x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 2.8125x + x2 = 9 The x term is 2.8125x. Take half its coefficient (1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. 2.8125x + 1.977539063 + x2 = 9 + 1.977539063 Reorder the terms: 1.977539063 + 2.8125x + x2 = 9 + 1.977539063 Combine like terms: 9 + 1.977539063 = 10.977539063 1.977539063 + 2.8125x + x2 = 10.977539063 Factor a perfect square on the left side: (x + 1.40625)(x + 1.40625) = 10.977539063 Calculate the square root of the right side: 3.313236946 Break this problem into two subproblems by setting (x + 1.40625) equal to 3.313236946 and -3.313236946.Subproblem 1
x + 1.40625 = 3.313236946 Simplifying x + 1.40625 = 3.313236946 Reorder the terms: 1.40625 + x = 3.313236946 Solving 1.40625 + x = 3.313236946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.40625' to each side of the equation. 1.40625 + -1.40625 + x = 3.313236946 + -1.40625 Combine like terms: 1.40625 + -1.40625 = 0.00000 0.00000 + x = 3.313236946 + -1.40625 x = 3.313236946 + -1.40625 Combine like terms: 3.313236946 + -1.40625 = 1.906986946 x = 1.906986946 Simplifying x = 1.906986946Subproblem 2
x + 1.40625 = -3.313236946 Simplifying x + 1.40625 = -3.313236946 Reorder the terms: 1.40625 + x = -3.313236946 Solving 1.40625 + x = -3.313236946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.40625' to each side of the equation. 1.40625 + -1.40625 + x = -3.313236946 + -1.40625 Combine like terms: 1.40625 + -1.40625 = 0.00000 0.00000 + x = -3.313236946 + -1.40625 x = -3.313236946 + -1.40625 Combine like terms: -3.313236946 + -1.40625 = -4.719486946 x = -4.719486946 Simplifying x = -4.719486946Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.906986946, -4.719486946}Solution
x = {0, 1.906986946, -4.719486946}
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