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Simplifying (X + -2)(X + 5) = 15 Reorder the terms: (-2 + X)(X + 5) = 15 Reorder the terms: (-2 + X)(5 + X) = 15 Multiply (-2 + X) * (5 + X) (-2(5 + X) + X(5 + X)) = 15 ((5 * -2 + X * -2) + X(5 + X)) = 15 ((-10 + -2X) + X(5 + X)) = 15 (-10 + -2X + (5 * X + X * X)) = 15 (-10 + -2X + (5X + X2)) = 15 Combine like terms: -2X + 5X = 3X (-10 + 3X + X2) = 15 Solving -10 + 3X + X2 = 15 Solving for variable 'X'. Reorder the terms: -10 + -15 + 3X + X2 = 15 + -15 Combine like terms: -10 + -15 = -25 -25 + 3X + X2 = 15 + -15 Combine like terms: 15 + -15 = 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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