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Simplifying -7.5x2 + -45x + 5400 = 0 Reorder the terms: 5400 + -45x + -7.5x2 = 0 Solving 5400 + -45x + -7.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7.5 the coefficient of the squared term: Divide each side by '-7.5'. -720 + 6x + x2 = 0 Move the constant term to the right: Add '720' to each side of the equation. -720 + 6x + 720 + x2 = 0 + 720 Reorder the terms: -720 + 720 + 6x + x2 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + 6x + x2 = 0 + 720 6x + x2 = 0 + 720 Combine like terms: 0 + 720 = 720 6x + x2 = 720 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 720 + 9 Reorder the terms: 9 + 6x + x2 = 720 + 9 Combine like terms: 720 + 9 = 729 9 + 6x + x2 = 729 Factor a perfect square on the left side: (x + 3)(x + 3) = 729 Calculate the square root of the right side: 27 Break this problem into two subproblems by setting (x + 3) equal to 27 and -27.Subproblem 1
x + 3 = 27 Simplifying x + 3 = 27 Reorder the terms: 3 + x = 27 Solving 3 + x = 27 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 27 + -3 Combine like terms: 3 + -3 = 0 0 + x = 27 + -3 x = 27 + -3 Combine like terms: 27 + -3 = 24 x = 24 Simplifying x = 24Subproblem 2
x + 3 = -27 Simplifying x + 3 = -27 Reorder the terms: 3 + x = -27 Solving 3 + x = -27 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -27 + -3 Combine like terms: 3 + -3 = 0 0 + x = -27 + -3 x = -27 + -3 Combine like terms: -27 + -3 = -30 x = -30 Simplifying x = -30Solution
The solution to the problem is based on the solutions from the subproblems. x = {24, -30}
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