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Simplifying x2 + -3x = 350 Reorder the terms: -3x + x2 = 350 Solving -3x + x2 = 350 Solving for variable 'x'. Reorder the terms: -350 + -3x + x2 = 350 + -350 Combine like terms: 350 + -350 = 0 -350 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + -3x + 350 + x2 = 0 + 350 Reorder the terms: -350 + 350 + -3x + x2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + -3x + x2 = 0 + 350 -3x + x2 = 0 + 350 Combine like terms: 0 + 350 = 350 -3x + x2 = 350 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 = 350 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 350 + 2.25 Combine like terms: 350 + 2.25 = 352.25 2.25 + -3x + x2 = 352.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 352.25 Calculate the square root of the right side: 18.768324379 Break this problem into two subproblems by setting (x + -1.5) equal to 18.768324379 and -18.768324379.Subproblem 1
x + -1.5 = 18.768324379 Simplifying x + -1.5 = 18.768324379 Reorder the terms: -1.5 + x = 18.768324379 Solving -1.5 + x = 18.768324379 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 = 18.768324379 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 18.768324379 + 1.5 x = 18.768324379 + 1.5 Combine like terms: 18.768324379 + 1.5 = 20.268324379 x = 20.268324379 Simplifying x = 20.268324379Subproblem 2
x + -1.5 = -18.768324379 Simplifying x + -1.5 = -18.768324379 Reorder the terms: -1.5 + x = -18.768324379 Solving -1.5 + x = -18.768324379 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 = -18.768324379 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -18.768324379 + 1.5 x = -18.768324379 + 1.5 Combine like terms: -18.768324379 + 1.5 = -17.268324379 x = -17.268324379 Simplifying x = -17.268324379Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.268324379, -17.268324379}
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