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Simplifying x2 + 3x = 420 Reorder the terms: 3x + x2 = 420 Solving 3x + x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + 3x + x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '420' to each side of the equation. -420 + 3x + 420 + x2 = 0 + 420 Reorder the terms: -420 + 420 + 3x + x2 = 0 + 420 Combine like terms: -420 + 420 = 0 0 + 3x + x2 = 0 + 420 3x + x2 = 0 + 420 Combine like terms: 0 + 420 = 420 3x + x2 = 420 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 = 420 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 420 + 2.25 Combine like terms: 420 + 2.25 = 422.25 2.25 + 3x + x2 = 422.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 422.25 Calculate the square root of the right side: 20.548722588 Break this problem into two subproblems by setting (x + 1.5) equal to 20.548722588 and -20.548722588.Subproblem 1
x + 1.5 = 20.548722588 Simplifying x + 1.5 = 20.548722588 Reorder the terms: 1.5 + x = 20.548722588 Solving 1.5 + x = 20.548722588 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 = 20.548722588 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 20.548722588 + -1.5 x = 20.548722588 + -1.5 Combine like terms: 20.548722588 + -1.5 = 19.048722588 x = 19.048722588 Simplifying x = 19.048722588Subproblem 2
x + 1.5 = -20.548722588 Simplifying x + 1.5 = -20.548722588 Reorder the terms: 1.5 + x = -20.548722588 Solving 1.5 + x = -20.548722588 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 = -20.548722588 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -20.548722588 + -1.5 x = -20.548722588 + -1.5 Combine like terms: -20.548722588 + -1.5 = -22.048722588 x = -22.048722588 Simplifying x = -22.048722588Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.048722588, -22.048722588}
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