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Simplifying 25x2 + -24x + -9 = 7x + 12x + -18 Reorder the terms: -9 + -24x + 25x2 = 7x + 12x + -18 Reorder the terms: -9 + -24x + 25x2 = -18 + 7x + 12x Combine like terms: 7x + 12x = 19x -9 + -24x + 25x2 = -18 + 19x Solving -9 + -24x + 25x2 = -18 + 19x Solving for variable 'x'. Reorder the terms: -9 + 18 + -24x + -19x + 25x2 = -18 + 19x + 18 + -19x Combine like terms: -9 + 18 = 9 9 + -24x + -19x + 25x2 = -18 + 19x + 18 + -19x Combine like terms: -24x + -19x = -43x 9 + -43x + 25x2 = -18 + 19x + 18 + -19x Reorder the terms: 9 + -43x + 25x2 = -18 + 18 + 19x + -19x Combine like terms: -18 + 18 = 0 9 + -43x + 25x2 = 0 + 19x + -19x 9 + -43x + 25x2 = 19x + -19x Combine like terms: 19x + -19x = 0 9 + -43x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.36 + -1.72x + x2 = 0 Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + -1.72x + -0.36 + x2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + -1.72x + x2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + -1.72x + x2 = 0 + -0.36 -1.72x + x2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 -1.72x + x2 = -0.36 The x term is -1.72x. Take half its coefficient (-0.86). Square it (0.7396) and add it to both sides. Add '0.7396' to each side of the equation. -1.72x + 0.7396 + x2 = -0.36 + 0.7396 Reorder the terms: 0.7396 + -1.72x + x2 = -0.36 + 0.7396 Combine like terms: -0.36 + 0.7396 = 0.3796 0.7396 + -1.72x + x2 = 0.3796 Factor a perfect square on the left side: (x + -0.86)(x + -0.86) = 0.3796 Calculate the square root of the right side: 0.616116872 Break this problem into two subproblems by setting (x + -0.86) equal to 0.616116872 and -0.616116872.Subproblem 1
x + -0.86 = 0.616116872 Simplifying x + -0.86 = 0.616116872 Reorder the terms: -0.86 + x = 0.616116872 Solving -0.86 + x = 0.616116872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.86' to each side of the equation. -0.86 + 0.86 + x = 0.616116872 + 0.86 Combine like terms: -0.86 + 0.86 = 0.00 0.00 + x = 0.616116872 + 0.86 x = 0.616116872 + 0.86 Combine like terms: 0.616116872 + 0.86 = 1.476116872 x = 1.476116872 Simplifying x = 1.476116872Subproblem 2
x + -0.86 = -0.616116872 Simplifying x + -0.86 = -0.616116872 Reorder the terms: -0.86 + x = -0.616116872 Solving -0.86 + x = -0.616116872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.86' to each side of the equation. -0.86 + 0.86 + x = -0.616116872 + 0.86 Combine like terms: -0.86 + 0.86 = 0.00 0.00 + x = -0.616116872 + 0.86 x = -0.616116872 + 0.86 Combine like terms: -0.616116872 + 0.86 = 0.243883128 x = 0.243883128 Simplifying x = 0.243883128Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.476116872, 0.243883128}
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