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Simplifying x2 + 3x = 312 Reorder the terms: 3x + x2 = 312 Solving 3x + x2 = 312 Solving for variable 'x'. Reorder the terms: -312 + 3x + x2 = 312 + -312 Combine like terms: 312 + -312 = 0 -312 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '312' to each side of the equation. -312 + 3x + 312 + x2 = 0 + 312 Reorder the terms: -312 + 312 + 3x + x2 = 0 + 312 Combine like terms: -312 + 312 = 0 0 + 3x + x2 = 0 + 312 3x + x2 = 0 + 312 Combine like terms: 0 + 312 = 312 3x + x2 = 312 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 = 312 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 312 + 2.25 Combine like terms: 312 + 2.25 = 314.25 2.25 + 3x + x2 = 314.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 314.25 Calculate the square root of the right side: 17.727097901 Break this problem into two subproblems by setting (x + 1.5) equal to 17.727097901 and -17.727097901.Subproblem 1
x + 1.5 = 17.727097901 Simplifying x + 1.5 = 17.727097901 Reorder the terms: 1.5 + x = 17.727097901 Solving 1.5 + x = 17.727097901 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 = 17.727097901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 17.727097901 + -1.5 x = 17.727097901 + -1.5 Combine like terms: 17.727097901 + -1.5 = 16.227097901 x = 16.227097901 Simplifying x = 16.227097901Subproblem 2
x + 1.5 = -17.727097901 Simplifying x + 1.5 = -17.727097901 Reorder the terms: 1.5 + x = -17.727097901 Solving 1.5 + x = -17.727097901 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 = -17.727097901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -17.727097901 + -1.5 x = -17.727097901 + -1.5 Combine like terms: -17.727097901 + -1.5 = -19.227097901 x = -19.227097901 Simplifying x = -19.227097901Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.227097901, -19.227097901}
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