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Simplifying X(X + 7) + -2 = 8 Reorder the terms: X(7 + X) + -2 = 8 (7 * X + X * X) + -2 = 8 (7X + X2) + -2 = 8 Reorder the terms: -2 + 7X + X2 = 8 Solving -2 + 7X + X2 = 8 Solving for variable 'X'. Reorder the terms: -2 + -8 + 7X + X2 = 8 + -8 Combine like terms: -2 + -8 = -10 -10 + 7X + X2 = 8 + -8 Combine like terms: 8 + -8 = 0 -10 + 7X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 7X + 10 + X2 = 0 + 10 Reorder the terms: -10 + 10 + 7X + X2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7X + X2 = 0 + 10 7X + X2 = 0 + 10 Combine like terms: 0 + 10 = 10 7X + X2 = 10 The X term is 7X. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7X + 12.25 + X2 = 10 + 12.25 Reorder the terms: 12.25 + 7X + X2 = 10 + 12.25 Combine like terms: 10 + 12.25 = 22.25 12.25 + 7X + X2 = 22.25 Factor a perfect square on the left side: (X + 3.5)(X + 3.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (X + 3.5) equal to 4.716990566 and -4.716990566.Subproblem 1
X + 3.5 = 4.716990566 Simplifying X + 3.5 = 4.716990566 Reorder the terms: 3.5 + X = 4.716990566 Solving 3.5 + X = 4.716990566 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = 4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = 4.716990566 + -3.5 X = 4.716990566 + -3.5 Combine like terms: 4.716990566 + -3.5 = 1.216990566 X = 1.216990566 Simplifying X = 1.216990566Subproblem 2
X + 3.5 = -4.716990566 Simplifying X + 3.5 = -4.716990566 Reorder the terms: 3.5 + X = -4.716990566 Solving 3.5 + X = -4.716990566 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = -4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = -4.716990566 + -3.5 X = -4.716990566 + -3.5 Combine like terms: -4.716990566 + -3.5 = -8.216990566 X = -8.216990566 Simplifying X = -8.216990566Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.216990566, -8.216990566}
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