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Simplifying x * x + 3x + -246 = 0 Multiply x * x x2 + 3x + -246 = 0 Reorder the terms: -246 + 3x + x2 = 0 Solving -246 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '246' to each side of the equation. -246 + 3x + 246 + x2 = 0 + 246 Reorder the terms: -246 + 246 + 3x + x2 = 0 + 246 Combine like terms: -246 + 246 = 0 0 + 3x + x2 = 0 + 246 3x + x2 = 0 + 246 Combine like terms: 0 + 246 = 246 3x + x2 = 246 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 = 246 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 246 + 2.25 Combine like terms: 246 + 2.25 = 248.25 2.25 + 3x + x2 = 248.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 248.25 Calculate the square root of the right side: 15.755951257 Break this problem into two subproblems by setting (x + 1.5) equal to 15.755951257 and -15.755951257.Subproblem 1
x + 1.5 = 15.755951257 Simplifying x + 1.5 = 15.755951257 Reorder the terms: 1.5 + x = 15.755951257 Solving 1.5 + x = 15.755951257 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 = 15.755951257 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 15.755951257 + -1.5 x = 15.755951257 + -1.5 Combine like terms: 15.755951257 + -1.5 = 14.255951257 x = 14.255951257 Simplifying x = 14.255951257Subproblem 2
x + 1.5 = -15.755951257 Simplifying x + 1.5 = -15.755951257 Reorder the terms: 1.5 + x = -15.755951257 Solving 1.5 + x = -15.755951257 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 = -15.755951257 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -15.755951257 + -1.5 x = -15.755951257 + -1.5 Combine like terms: -15.755951257 + -1.5 = -17.255951257 x = -17.255951257 Simplifying x = -17.255951257Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.255951257, -17.255951257}
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