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Simplifying (X + 7)(X + -3) = 12 Reorder the terms: (7 + X)(X + -3) = 12 Reorder the terms: (7 + X)(-3 + X) = 12 Multiply (7 + X) * (-3 + X) (7(-3 + X) + X(-3 + X)) = 12 ((-3 * 7 + X * 7) + X(-3 + X)) = 12 ((-21 + 7X) + X(-3 + X)) = 12 (-21 + 7X + (-3 * X + X * X)) = 12 (-21 + 7X + (-3X + X2)) = 12 Combine like terms: 7X + -3X = 4X (-21 + 4X + X2) = 12 Solving -21 + 4X + X2 = 12 Solving for variable 'X'. Reorder the terms: -21 + -12 + 4X + X2 = 12 + -12 Combine like terms: -21 + -12 = -33 -33 + 4X + X2 = 12 + -12 Combine like terms: 12 + -12 = 0 -33 + 4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 4X + 33 + X2 = 0 + 33 Reorder the terms: -33 + 33 + 4X + X2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 4X + X2 = 0 + 33 4X + X2 = 0 + 33 Combine like terms: 0 + 33 = 33 4X + X2 = 33 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 33 + 4 Reorder the terms: 4 + 4X + X2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + 4X + X2 = 37 Factor a perfect square on the left side: (X + 2)(X + 2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (X + 2) equal to 6.08276253 and -6.08276253.Subproblem 1
X + 2 = 6.08276253 Simplifying X + 2 = 6.08276253 Reorder the terms: 2 + X = 6.08276253 Solving 2 + X = 6.08276253 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + X = 6.08276253 + -2 X = 6.08276253 + -2 Combine like terms: 6.08276253 + -2 = 4.08276253 X = 4.08276253 Simplifying X = 4.08276253Subproblem 2
X + 2 = -6.08276253 Simplifying X + 2 = -6.08276253 Reorder the terms: 2 + X = -6.08276253 Solving 2 + X = -6.08276253 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + X = -6.08276253 + -2 X = -6.08276253 + -2 Combine like terms: -6.08276253 + -2 = -8.08276253 X = -8.08276253 Simplifying X = -8.08276253Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.08276253, -8.08276253}
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