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Simplifying -3.75x2 + 7.5x + 1980 = 0 Reorder the terms: 1980 + 7.5x + -3.75x2 = 0 Solving 1980 + 7.5x + -3.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.75 the coefficient of the squared term: Divide each side by '-3.75'. -528 + -2x + x2 = 0 Move the constant term to the right: Add '528' to each side of the equation. -528 + -2x + 528 + x2 = 0 + 528 Reorder the terms: -528 + 528 + -2x + x2 = 0 + 528 Combine like terms: -528 + 528 = 0 0 + -2x + x2 = 0 + 528 -2x + x2 = 0 + 528 Combine like terms: 0 + 528 = 528 -2x + x2 = 528 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 528 + 1 Reorder the terms: 1 + -2x + x2 = 528 + 1 Combine like terms: 528 + 1 = 529 1 + -2x + x2 = 529 Factor a perfect square on the left side: (x + -1)(x + -1) = 529 Calculate the square root of the right side: 23 Break this problem into two subproblems by setting (x + -1) equal to 23 and -23.Subproblem 1
x + -1 = 23 Simplifying x + -1 = 23 Reorder the terms: -1 + x = 23 Solving -1 + x = 23 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 23 + 1 Combine like terms: -1 + 1 = 0 0 + x = 23 + 1 x = 23 + 1 Combine like terms: 23 + 1 = 24 x = 24 Simplifying x = 24Subproblem 2
x + -1 = -23 Simplifying x + -1 = -23 Reorder the terms: -1 + x = -23 Solving -1 + x = -23 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -23 + 1 Combine like terms: -1 + 1 = 0 0 + x = -23 + 1 x = -23 + 1 Combine like terms: -23 + 1 = -22 x = -22 Simplifying x = -22Solution
The solution to the problem is based on the solutions from the subproblems. x = {24, -22}
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