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Simplifying 25x2 + -15x + -64 = 5x + -10 Reorder the terms: -64 + -15x + 25x2 = 5x + -10 Reorder the terms: -64 + -15x + 25x2 = -10 + 5x Solving -64 + -15x + 25x2 = -10 + 5x Solving for variable 'x'. Reorder the terms: -64 + 10 + -15x + -5x + 25x2 = -10 + 5x + 10 + -5x Combine like terms: -64 + 10 = -54 -54 + -15x + -5x + 25x2 = -10 + 5x + 10 + -5x Combine like terms: -15x + -5x = -20x -54 + -20x + 25x2 = -10 + 5x + 10 + -5x Reorder the terms: -54 + -20x + 25x2 = -10 + 10 + 5x + -5x Combine like terms: -10 + 10 = 0 -54 + -20x + 25x2 = 0 + 5x + -5x -54 + -20x + 25x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -54 + -20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.16 + -0.8x + x2 = 0 Move the constant term to the right: Add '2.16' to each side of the equation. -2.16 + -0.8x + 2.16 + x2 = 0 + 2.16 Reorder the terms: -2.16 + 2.16 + -0.8x + x2 = 0 + 2.16 Combine like terms: -2.16 + 2.16 = 0.00 0.00 + -0.8x + x2 = 0 + 2.16 -0.8x + x2 = 0 + 2.16 Combine like terms: 0 + 2.16 = 2.16 -0.8x + x2 = 2.16 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 2.16 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 2.16 + 0.16 Combine like terms: 2.16 + 0.16 = 2.32 0.16 + -0.8x + x2 = 2.32 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 2.32 Calculate the square root of the right side: 1.523154621 Break this problem into two subproblems by setting (x + -0.4) equal to 1.523154621 and -1.523154621.Subproblem 1
x + -0.4 = 1.523154621 Simplifying x + -0.4 = 1.523154621 Reorder the terms: -0.4 + x = 1.523154621 Solving -0.4 + x = 1.523154621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.523154621 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.523154621 + 0.4 x = 1.523154621 + 0.4 Combine like terms: 1.523154621 + 0.4 = 1.923154621 x = 1.923154621 Simplifying x = 1.923154621Subproblem 2
x + -0.4 = -1.523154621 Simplifying x + -0.4 = -1.523154621 Reorder the terms: -0.4 + x = -1.523154621 Solving -0.4 + x = -1.523154621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.523154621 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.523154621 + 0.4 x = -1.523154621 + 0.4 Combine like terms: -1.523154621 + 0.4 = -1.123154621 x = -1.123154621 Simplifying x = -1.123154621Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.923154621, -1.123154621}
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