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Simplifying (2x + 3)(x + 3) = 60 Reorder the terms: (3 + 2x)(x + 3) = 60 Reorder the terms: (3 + 2x)(3 + x) = 60 Multiply (3 + 2x) * (3 + x) (3(3 + x) + 2x * (3 + x)) = 60 ((3 * 3 + x * 3) + 2x * (3 + x)) = 60 ((9 + 3x) + 2x * (3 + x)) = 60 (9 + 3x + (3 * 2x + x * 2x)) = 60 (9 + 3x + (6x + 2x2)) = 60 Combine like terms: 3x + 6x = 9x (9 + 9x + 2x2) = 60 Solving 9 + 9x + 2x2 = 60 Solving for variable 'x'. Reorder the terms: 9 + -60 + 9x + 2x2 = 60 + -60 Combine like terms: 9 + -60 = -51 -51 + 9x + 2x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -51 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + 4.5x + 25.5 + x2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + 4.5x + x2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + 4.5x + x2 = 0 + 25.5 4.5x + x2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 4.5x + x2 = 25.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 25.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 25.5 + 5.0625 Combine like terms: 25.5 + 5.0625 = 30.5625 5.0625 + 4.5x + x2 = 30.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (x + 2.25) equal to 5.528336097 and -5.528336097.Subproblem 1
x + 2.25 = 5.528336097 Simplifying x + 2.25 = 5.528336097 Reorder the terms: 2.25 + x = 5.528336097 Solving 2.25 + x = 5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 5.528336097 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 5.528336097 + -2.25 x = 5.528336097 + -2.25 Combine like terms: 5.528336097 + -2.25 = 3.278336097 x = 3.278336097 Simplifying x = 3.278336097Subproblem 2
x + 2.25 = -5.528336097 Simplifying x + 2.25 = -5.528336097 Reorder the terms: 2.25 + x = -5.528336097 Solving 2.25 + x = -5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -5.528336097 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -5.528336097 + -2.25 x = -5.528336097 + -2.25 Combine like terms: -5.528336097 + -2.25 = -7.778336097 x = -7.778336097 Simplifying x = -7.778336097Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.278336097, -7.778336097}
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