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Simplifying x2 + 3x = 334 Reorder the terms: 3x + x2 = 334 Solving 3x + x2 = 334 Solving for variable 'x'. Reorder the terms: -334 + 3x + x2 = 334 + -334 Combine like terms: 334 + -334 = 0 -334 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '334' to each side of the equation. -334 + 3x + 334 + x2 = 0 + 334 Reorder the terms: -334 + 334 + 3x + x2 = 0 + 334 Combine like terms: -334 + 334 = 0 0 + 3x + x2 = 0 + 334 3x + x2 = 0 + 334 Combine like terms: 0 + 334 = 334 3x + x2 = 334 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 = 334 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 334 + 2.25 Combine like terms: 334 + 2.25 = 336.25 2.25 + 3x + x2 = 336.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 336.25 Calculate the square root of the right side: 18.337120821 Break this problem into two subproblems by setting (x + 1.5) equal to 18.337120821 and -18.337120821.Subproblem 1
x + 1.5 = 18.337120821 Simplifying x + 1.5 = 18.337120821 Reorder the terms: 1.5 + x = 18.337120821 Solving 1.5 + x = 18.337120821 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 = 18.337120821 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 18.337120821 + -1.5 x = 18.337120821 + -1.5 Combine like terms: 18.337120821 + -1.5 = 16.837120821 x = 16.837120821 Simplifying x = 16.837120821Subproblem 2
x + 1.5 = -18.337120821 Simplifying x + 1.5 = -18.337120821 Reorder the terms: 1.5 + x = -18.337120821 Solving 1.5 + x = -18.337120821 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 = -18.337120821 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -18.337120821 + -1.5 x = -18.337120821 + -1.5 Combine like terms: -18.337120821 + -1.5 = -19.837120821 x = -19.837120821 Simplifying x = -19.837120821Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.837120821, -19.837120821}
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