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Simplifying 29x2 + 7x + -3 = 0 Reorder the terms: -3 + 7x + 29x2 = 0 Solving -3 + 7x + 29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -0.1034482759 + 0.2413793103x + x2 = 0 Move the constant term to the right: Add '0.1034482759' to each side of the equation. -0.1034482759 + 0.2413793103x + 0.1034482759 + x2 = 0 + 0.1034482759 Reorder the terms: -0.1034482759 + 0.1034482759 + 0.2413793103x + x2 = 0 + 0.1034482759 Combine like terms: -0.1034482759 + 0.1034482759 = 0.0000000000 0.0000000000 + 0.2413793103x + x2 = 0 + 0.1034482759 0.2413793103x + x2 = 0 + 0.1034482759 Combine like terms: 0 + 0.1034482759 = 0.1034482759 0.2413793103x + x2 = 0.1034482759 The x term is 0.2413793103x. Take half its coefficient (0.1206896552). Square it (0.01456599287) and add it to both sides. Add '0.01456599287' to each side of the equation. 0.2413793103x + 0.01456599287 + x2 = 0.1034482759 + 0.01456599287 Reorder the terms: 0.01456599287 + 0.2413793103x + x2 = 0.1034482759 + 0.01456599287 Combine like terms: 0.1034482759 + 0.01456599287 = 0.11801426877 0.01456599287 + 0.2413793103x + x2 = 0.11801426877 Factor a perfect square on the left side: (x + 0.1206896552)(x + 0.1206896552) = 0.11801426877 Calculate the square root of the right side: 0.343532049 Break this problem into two subproblems by setting (x + 0.1206896552) equal to 0.343532049 and -0.343532049.Subproblem 1
x + 0.1206896552 = 0.343532049 Simplifying x + 0.1206896552 = 0.343532049 Reorder the terms: 0.1206896552 + x = 0.343532049 Solving 0.1206896552 + x = 0.343532049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1206896552' to each side of the equation. 0.1206896552 + -0.1206896552 + x = 0.343532049 + -0.1206896552 Combine like terms: 0.1206896552 + -0.1206896552 = 0.0000000000 0.0000000000 + x = 0.343532049 + -0.1206896552 x = 0.343532049 + -0.1206896552 Combine like terms: 0.343532049 + -0.1206896552 = 0.2228423938 x = 0.2228423938 Simplifying x = 0.2228423938Subproblem 2
x + 0.1206896552 = -0.343532049 Simplifying x + 0.1206896552 = -0.343532049 Reorder the terms: 0.1206896552 + x = -0.343532049 Solving 0.1206896552 + x = -0.343532049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1206896552' to each side of the equation. 0.1206896552 + -0.1206896552 + x = -0.343532049 + -0.1206896552 Combine like terms: 0.1206896552 + -0.1206896552 = 0.0000000000 0.0000000000 + x = -0.343532049 + -0.1206896552 x = -0.343532049 + -0.1206896552 Combine like terms: -0.343532049 + -0.1206896552 = -0.4642217042 x = -0.4642217042 Simplifying x = -0.4642217042Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2228423938, -0.4642217042}
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