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Simplifying x(x + 3) = 96 Reorder the terms: x(3 + x) = 96 (3 * x + x * x) = 96 (3x + x2) = 96 Solving 3x + x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + 3x + x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 3x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 3x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 3x + x2 = 0 + 96 3x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 3x + x2 = 96 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 96 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 96 + 2.25 Combine like terms: 96 + 2.25 = 98.25 2.25 + 3x + x2 = 98.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (x + 1.5) equal to 9.912113801 and -9.912113801.Subproblem 1
x + 1.5 = 9.912113801 Simplifying x + 1.5 = 9.912113801 Reorder the terms: 1.5 + x = 9.912113801 Solving 1.5 + x = 9.912113801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.912113801 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.912113801 + -1.5 x = 9.912113801 + -1.5 Combine like terms: 9.912113801 + -1.5 = 8.412113801 x = 8.412113801 Simplifying x = 8.412113801Subproblem 2
x + 1.5 = -9.912113801 Simplifying x + 1.5 = -9.912113801 Reorder the terms: 1.5 + x = -9.912113801 Solving 1.5 + x = -9.912113801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.912113801 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.912113801 + -1.5 x = -9.912113801 + -1.5 Combine like terms: -9.912113801 + -1.5 = -11.412113801 x = -11.412113801 Simplifying x = -11.412113801Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.412113801, -11.412113801}
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