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Simplifying 0 = -7.5(x2 + -4x + -320) Reorder the terms: 0 = -7.5(-320 + -4x + x2) 0 = (-320 * -7.5 + -4x * -7.5 + x2 * -7.5) 0 = (2400 + 30x + -7.5x2) Solving 0 = 2400 + 30x + -7.5x2 Solving for variable 'x'. Combine like terms: 0 + -2400 = -2400 -2400 + -30x + 7.5x2 = 2400 + 30x + -7.5x2 + -2400 + -30x + 7.5x2 Reorder the terms: -2400 + -30x + 7.5x2 = 2400 + -2400 + 30x + -30x + -7.5x2 + 7.5x2 Combine like terms: 2400 + -2400 = 0 -2400 + -30x + 7.5x2 = 0 + 30x + -30x + -7.5x2 + 7.5x2 -2400 + -30x + 7.5x2 = 30x + -30x + -7.5x2 + 7.5x2 Combine like terms: 30x + -30x = 0 -2400 + -30x + 7.5x2 = 0 + -7.5x2 + 7.5x2 -2400 + -30x + 7.5x2 = -7.5x2 + 7.5x2 Combine like terms: -7.5x2 + 7.5x2 = 0.0 -2400 + -30x + 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'. -320 + -4x + x2 = 0 Move the constant term to the right: Add '320' to each side of the equation. -320 + -4x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + -4x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + -4x + x2 = 0 + 320 -4x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 -4x + x2 = 320 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 320 + 4 Reorder the terms: 4 + -4x + x2 = 320 + 4 Combine like terms: 320 + 4 = 324 4 + -4x + x2 = 324 Factor a perfect square on the left side: (x + -2)(x + -2) = 324 Calculate the square root of the right side: 18 Break this problem into two subproblems by setting (x + -2) equal to 18 and -18.Subproblem 1
x + -2 = 18 Simplifying x + -2 = 18 Reorder the terms: -2 + x = 18 Solving -2 + x = 18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 18 + 2 Combine like terms: -2 + 2 = 0 0 + x = 18 + 2 x = 18 + 2 Combine like terms: 18 + 2 = 20 x = 20 Simplifying x = 20Subproblem 2
x + -2 = -18 Simplifying x + -2 = -18 Reorder the terms: -2 + x = -18 Solving -2 + x = -18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -18 + 2 Combine like terms: -2 + 2 = 0 0 + x = -18 + 2 x = -18 + 2 Combine like terms: -18 + 2 = -16 x = -16 Simplifying x = -16Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -16}
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