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Simplifying x2 + -3x + -348 = 0 Reorder the terms: -348 + -3x + x2 = 0 Solving -348 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '348' to each side of the equation. -348 + -3x + 348 + x2 = 0 + 348 Reorder the terms: -348 + 348 + -3x + x2 = 0 + 348 Combine like terms: -348 + 348 = 0 0 + -3x + x2 = 0 + 348 -3x + x2 = 0 + 348 Combine like terms: 0 + 348 = 348 -3x + x2 = 348 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 = 348 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 348 + 2.25 Combine like terms: 348 + 2.25 = 350.25 2.25 + -3x + x2 = 350.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 350.25 Calculate the square root of the right side: 18.714967272 Break this problem into two subproblems by setting (x + -1.5) equal to 18.714967272 and -18.714967272.Subproblem 1
x + -1.5 = 18.714967272 Simplifying x + -1.5 = 18.714967272 Reorder the terms: -1.5 + x = 18.714967272 Solving -1.5 + x = 18.714967272 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 = 18.714967272 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 18.714967272 + 1.5 x = 18.714967272 + 1.5 Combine like terms: 18.714967272 + 1.5 = 20.214967272 x = 20.214967272 Simplifying x = 20.214967272Subproblem 2
x + -1.5 = -18.714967272 Simplifying x + -1.5 = -18.714967272 Reorder the terms: -1.5 + x = -18.714967272 Solving -1.5 + x = -18.714967272 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 = -18.714967272 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -18.714967272 + 1.5 x = -18.714967272 + 1.5 Combine like terms: -18.714967272 + 1.5 = -17.214967272 x = -17.214967272 Simplifying x = -17.214967272Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.214967272, -17.214967272}
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