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Simplifying 25x2 + -24x + -9 = -7x2 + 12 + -18 Reorder the terms: -9 + -24x + 25x2 = -7x2 + 12 + -18 Reorder the terms: -9 + -24x + 25x2 = 12 + -18 + -7x2 Combine like terms: 12 + -18 = -6 -9 + -24x + 25x2 = -6 + -7x2 Solving -9 + -24x + 25x2 = -6 + -7x2 Solving for variable 'x'. Reorder the terms: -9 + 6 + -24x + 25x2 + 7x2 = -6 + -7x2 + 6 + 7x2 Combine like terms: -9 + 6 = -3 -3 + -24x + 25x2 + 7x2 = -6 + -7x2 + 6 + 7x2 Combine like terms: 25x2 + 7x2 = 32x2 -3 + -24x + 32x2 = -6 + -7x2 + 6 + 7x2 Reorder the terms: -3 + -24x + 32x2 = -6 + 6 + -7x2 + 7x2 Combine like terms: -6 + 6 = 0 -3 + -24x + 32x2 = 0 + -7x2 + 7x2 -3 + -24x + 32x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -3 + -24x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.09375 + -0.75x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -0.75x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -0.75x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -0.75x + x2 = 0 + 0.09375 -0.75x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -0.75x + x2 = 0.09375 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 0.09375 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.09375 + 0.140625 Combine like terms: 0.09375 + 0.140625 = 0.234375 0.140625 + -0.75x + x2 = 0.234375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.234375 Calculate the square root of the right side: 0.484122918 Break this problem into two subproblems by setting (x + -0.375) equal to 0.484122918 and -0.484122918.Subproblem 1
x + -0.375 = 0.484122918 Simplifying x + -0.375 = 0.484122918 Reorder the terms: -0.375 + x = 0.484122918 Solving -0.375 + x = 0.484122918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.484122918 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.484122918 + 0.375 x = 0.484122918 + 0.375 Combine like terms: 0.484122918 + 0.375 = 0.859122918 x = 0.859122918 Simplifying x = 0.859122918Subproblem 2
x + -0.375 = -0.484122918 Simplifying x + -0.375 = -0.484122918 Reorder the terms: -0.375 + x = -0.484122918 Solving -0.375 + x = -0.484122918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.484122918 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.484122918 + 0.375 x = -0.484122918 + 0.375 Combine like terms: -0.484122918 + 0.375 = -0.109122918 x = -0.109122918 Simplifying x = -0.109122918Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.859122918, -0.109122918}
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