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Simplifying x + 3x + 2x2 = 840 Combine like terms: x + 3x = 4x 4x + 2x2 = 840 Solving 4x + 2x2 = 840 Solving for variable 'x'. Reorder the terms: -840 + 4x + 2x2 = 840 + -840 Combine like terms: 840 + -840 = 0 -840 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-420 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-420 + 2x + x2)' equal to zero and attempt to solve: Simplifying -420 + 2x + x2 = 0 Solving -420 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '420' to each side of the equation. -420 + 2x + 420 + x2 = 0 + 420 Reorder the terms: -420 + 420 + 2x + x2 = 0 + 420 Combine like terms: -420 + 420 = 0 0 + 2x + x2 = 0 + 420 2x + x2 = 0 + 420 Combine like terms: 0 + 420 = 420 2x + x2 = 420 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 420 + 1 Reorder the terms: 1 + 2x + x2 = 420 + 1 Combine like terms: 420 + 1 = 421 1 + 2x + x2 = 421 Factor a perfect square on the left side: (x + 1)(x + 1) = 421 Calculate the square root of the right side: 20.518284529 Break this problem into two subproblems by setting (x + 1) equal to 20.518284529 and -20.518284529.Subproblem 1
x + 1 = 20.518284529 Simplifying x + 1 = 20.518284529 Reorder the terms: 1 + x = 20.518284529 Solving 1 + x = 20.518284529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 20.518284529 + -1 Combine like terms: 1 + -1 = 0 0 + x = 20.518284529 + -1 x = 20.518284529 + -1 Combine like terms: 20.518284529 + -1 = 19.518284529 x = 19.518284529 Simplifying x = 19.518284529Subproblem 2
x + 1 = -20.518284529 Simplifying x + 1 = -20.518284529 Reorder the terms: 1 + x = -20.518284529 Solving 1 + x = -20.518284529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -20.518284529 + -1 Combine like terms: 1 + -1 = 0 0 + x = -20.518284529 + -1 x = -20.518284529 + -1 Combine like terms: -20.518284529 + -1 = -21.518284529 x = -21.518284529 Simplifying x = -21.518284529Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.518284529, -21.518284529}Solution
x = {19.518284529, -21.518284529}
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