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Simplifying x * x + 3x + 3 = 294 Multiply x * x x2 + 3x + 3 = 294 Reorder the terms: 3 + 3x + x2 = 294 Solving 3 + 3x + x2 = 294 Solving for variable 'x'. Reorder the terms: 3 + -294 + 3x + x2 = 294 + -294 Combine like terms: 3 + -294 = -291 -291 + 3x + x2 = 294 + -294 Combine like terms: 294 + -294 = 0 -291 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '291' to each side of the equation. -291 + 3x + 291 + x2 = 0 + 291 Reorder the terms: -291 + 291 + 3x + x2 = 0 + 291 Combine like terms: -291 + 291 = 0 0 + 3x + x2 = 0 + 291 3x + x2 = 0 + 291 Combine like terms: 0 + 291 = 291 3x + x2 = 291 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 = 291 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 291 + 2.25 Combine like terms: 291 + 2.25 = 293.25 2.25 + 3x + x2 = 293.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 293.25 Calculate the square root of the right side: 17.12454379 Break this problem into two subproblems by setting (x + 1.5) equal to 17.12454379 and -17.12454379.Subproblem 1
x + 1.5 = 17.12454379 Simplifying x + 1.5 = 17.12454379 Reorder the terms: 1.5 + x = 17.12454379 Solving 1.5 + x = 17.12454379 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 = 17.12454379 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 17.12454379 + -1.5 x = 17.12454379 + -1.5 Combine like terms: 17.12454379 + -1.5 = 15.62454379 x = 15.62454379 Simplifying x = 15.62454379Subproblem 2
x + 1.5 = -17.12454379 Simplifying x + 1.5 = -17.12454379 Reorder the terms: 1.5 + x = -17.12454379 Solving 1.5 + x = -17.12454379 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 = -17.12454379 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -17.12454379 + -1.5 x = -17.12454379 + -1.5 Combine like terms: -17.12454379 + -1.5 = -18.62454379 x = -18.62454379 Simplifying x = -18.62454379Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.62454379, -18.62454379}
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