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Simplifying 0 = -7.5x2 + 60x + 9600 Reorder the terms: 0 = 9600 + 60x + -7.5x2 Solving 0 = 9600 + 60x + -7.5x2 Solving for variable 'x'. Combine like terms: 0 + -9600 = -9600 -9600 + -60x + 7.5x2 = 9600 + 60x + -7.5x2 + -9600 + -60x + 7.5x2 Reorder the terms: -9600 + -60x + 7.5x2 = 9600 + -9600 + 60x + -60x + -7.5x2 + 7.5x2 Combine like terms: 9600 + -9600 = 0 -9600 + -60x + 7.5x2 = 0 + 60x + -60x + -7.5x2 + 7.5x2 -9600 + -60x + 7.5x2 = 60x + -60x + -7.5x2 + 7.5x2 Combine like terms: 60x + -60x = 0 -9600 + -60x + 7.5x2 = 0 + -7.5x2 + 7.5x2 -9600 + -60x + 7.5x2 = -7.5x2 + 7.5x2 Combine like terms: -7.5x2 + 7.5x2 = 0.0 -9600 + -60x + 7.5x2 = 0.0 Begin completing the square. Divide all terms by 7.5 the coefficient of the squared term: Divide each side by '7.5'. -1280 + -8x + x2 = 0 Move the constant term to the right: Add '1280' to each side of the equation. -1280 + -8x + 1280 + x2 = 0 + 1280 Reorder the terms: -1280 + 1280 + -8x + x2 = 0 + 1280 Combine like terms: -1280 + 1280 = 0 0 + -8x + x2 = 0 + 1280 -8x + x2 = 0 + 1280 Combine like terms: 0 + 1280 = 1280 -8x + x2 = 1280 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 1280 + 16 Reorder the terms: 16 + -8x + x2 = 1280 + 16 Combine like terms: 1280 + 16 = 1296 16 + -8x + x2 = 1296 Factor a perfect square on the left side: (x + -4)(x + -4) = 1296 Calculate the square root of the right side: 36 Break this problem into two subproblems by setting (x + -4) equal to 36 and -36.Subproblem 1
x + -4 = 36 Simplifying x + -4 = 36 Reorder the terms: -4 + x = 36 Solving -4 + x = 36 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 36 + 4 Combine like terms: -4 + 4 = 0 0 + x = 36 + 4 x = 36 + 4 Combine like terms: 36 + 4 = 40 x = 40 Simplifying x = 40Subproblem 2
x + -4 = -36 Simplifying x + -4 = -36 Reorder the terms: -4 + x = -36 Solving -4 + x = -36 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -36 + 4 Combine like terms: -4 + 4 = 0 0 + x = -36 + 4 x = -36 + 4 Combine like terms: -36 + 4 = -32 x = -32 Simplifying x = -32Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, -32}
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