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Simplifying 7.25x2 + 25x + 16 = 0 Reorder the terms: 16 + 25x + 7.25x2 = 0 Solving 16 + 25x + 7.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.25 the coefficient of the squared term: Divide each side by '7.25'. 2.206896552 + 3.448275862x + x2 = 0 Move the constant term to the right: Add '-2.206896552' to each side of the equation. 2.206896552 + 3.448275862x + -2.206896552 + x2 = 0 + -2.206896552 Reorder the terms: 2.206896552 + -2.206896552 + 3.448275862x + x2 = 0 + -2.206896552 Combine like terms: 2.206896552 + -2.206896552 = 0.000000000 0.000000000 + 3.448275862x + x2 = 0 + -2.206896552 3.448275862x + x2 = 0 + -2.206896552 Combine like terms: 0 + -2.206896552 = -2.206896552 3.448275862x + x2 = -2.206896552 The x term is 3.448275862x. Take half its coefficient (1.724137931). Square it (2.972651605) and add it to both sides. Add '2.972651605' to each side of the equation. 3.448275862x + 2.972651605 + x2 = -2.206896552 + 2.972651605 Reorder the terms: 2.972651605 + 3.448275862x + x2 = -2.206896552 + 2.972651605 Combine like terms: -2.206896552 + 2.972651605 = 0.765755053 2.972651605 + 3.448275862x + x2 = 0.765755053 Factor a perfect square on the left side: (x + 1.724137931)(x + 1.724137931) = 0.765755053 Calculate the square root of the right side: 0.875074313 Break this problem into two subproblems by setting (x + 1.724137931) equal to 0.875074313 and -0.875074313.Subproblem 1
x + 1.724137931 = 0.875074313 Simplifying x + 1.724137931 = 0.875074313 Reorder the terms: 1.724137931 + x = 0.875074313 Solving 1.724137931 + x = 0.875074313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.724137931' to each side of the equation. 1.724137931 + -1.724137931 + x = 0.875074313 + -1.724137931 Combine like terms: 1.724137931 + -1.724137931 = 0.000000000 0.000000000 + x = 0.875074313 + -1.724137931 x = 0.875074313 + -1.724137931 Combine like terms: 0.875074313 + -1.724137931 = -0.849063618 x = -0.849063618 Simplifying x = -0.849063618Subproblem 2
x + 1.724137931 = -0.875074313 Simplifying x + 1.724137931 = -0.875074313 Reorder the terms: 1.724137931 + x = -0.875074313 Solving 1.724137931 + x = -0.875074313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.724137931' to each side of the equation. 1.724137931 + -1.724137931 + x = -0.875074313 + -1.724137931 Combine like terms: 1.724137931 + -1.724137931 = 0.000000000 0.000000000 + x = -0.875074313 + -1.724137931 x = -0.875074313 + -1.724137931 Combine like terms: -0.875074313 + -1.724137931 = -2.599212244 x = -2.599212244 Simplifying x = -2.599212244Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.849063618, -2.599212244}
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