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Simplifying 0.75x2 + -6x + -56 = 0.5x2 + -1x Reorder the terms: -56 + -6x + 0.75x2 = 0.5x2 + -1x Reorder the terms: -56 + -6x + 0.75x2 = -1x + 0.5x2 Solving -56 + -6x + 0.75x2 = -1x + 0.5x2 Solving for variable 'x'. Reorder the terms: -56 + -6x + x + 0.75x2 + -0.5x2 = -1x + 0.5x2 + x + -0.5x2 Combine like terms: -6x + x = -5x -56 + -5x + 0.75x2 + -0.5x2 = -1x + 0.5x2 + x + -0.5x2 Combine like terms: 0.75x2 + -0.5x2 = 0.25x2 -56 + -5x + 0.25x2 = -1x + 0.5x2 + x + -0.5x2 Reorder the terms: -56 + -5x + 0.25x2 = -1x + x + 0.5x2 + -0.5x2 Combine like terms: -1x + x = 0 -56 + -5x + 0.25x2 = 0 + 0.5x2 + -0.5x2 -56 + -5x + 0.25x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -56 + -5x + 0.25x2 = 0.0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -224 + -20x + x2 = 0 Move the constant term to the right: Add '224' to each side of the equation. -224 + -20x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + -20x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + -20x + x2 = 0 + 224 -20x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 -20x + x2 = 224 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 224 + 100 Reorder the terms: 100 + -20x + x2 = 224 + 100 Combine like terms: 224 + 100 = 324 100 + -20x + x2 = 324 Factor a perfect square on the left side: (x + -10)(x + -10) = 324 Calculate the square root of the right side: 18 Break this problem into two subproblems by setting (x + -10) equal to 18 and -18.Subproblem 1
x + -10 = 18 Simplifying x + -10 = 18 Reorder the terms: -10 + x = 18 Solving -10 + x = 18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 18 + 10 Combine like terms: -10 + 10 = 0 0 + x = 18 + 10 x = 18 + 10 Combine like terms: 18 + 10 = 28 x = 28 Simplifying x = 28Subproblem 2
x + -10 = -18 Simplifying x + -10 = -18 Reorder the terms: -10 + x = -18 Solving -10 + x = -18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -18 + 10 Combine like terms: -10 + 10 = 0 0 + x = -18 + 10 x = -18 + 10 Combine like terms: -18 + 10 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {28, -8}
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