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Simplifying x(x + 3) = 25 Reorder the terms: x(3 + x) = 25 (3 * x + x * x) = 25 (3x + x2) = 25 Solving 3x + x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 3x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 3x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 3x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 3x + x2 = 0 + 25 3x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 3x + x2 = 25 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 = 25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 25 + 2.25 Combine like terms: 25 + 2.25 = 27.25 2.25 + 3x + x2 = 27.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 1.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 1.5 = 5.220153254 Simplifying x + 1.5 = 5.220153254 Reorder the terms: 1.5 + x = 5.220153254 Solving 1.5 + x = 5.220153254 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 = 5.220153254 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.220153254 + -1.5 x = 5.220153254 + -1.5 Combine like terms: 5.220153254 + -1.5 = 3.720153254 x = 3.720153254 Simplifying x = 3.720153254Subproblem 2
x + 1.5 = -5.220153254 Simplifying x + 1.5 = -5.220153254 Reorder the terms: 1.5 + x = -5.220153254 Solving 1.5 + x = -5.220153254 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 = -5.220153254 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.220153254 + -1.5 x = -5.220153254 + -1.5 Combine like terms: -5.220153254 + -1.5 = -6.720153254 x = -6.720153254 Simplifying x = -6.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.720153254, -6.720153254}
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