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Simplifying (x + 7)(x + 7) + 1 = 12 Reorder the terms: (7 + x)(x + 7) + 1 = 12 Reorder the terms: (7 + x)(7 + x) + 1 = 12 Multiply (7 + x) * (7 + x) (7(7 + x) + x(7 + x)) + 1 = 12 ((7 * 7 + x * 7) + x(7 + x)) + 1 = 12 ((49 + 7x) + x(7 + x)) + 1 = 12 (49 + 7x + (7 * x + x * x)) + 1 = 12 (49 + 7x + (7x + x2)) + 1 = 12 Combine like terms: 7x + 7x = 14x (49 + 14x + x2) + 1 = 12 Reorder the terms: 49 + 1 + 14x + x2 = 12 Combine like terms: 49 + 1 = 50 50 + 14x + x2 = 12 Solving 50 + 14x + x2 = 12 Solving for variable 'x'. Reorder the terms: 50 + -12 + 14x + x2 = 12 + -12 Combine like terms: 50 + -12 = 38 38 + 14x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 38 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + 14x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + 14x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 14x + x2 = 0 + -38 14x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 14x + x2 = -38 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -38 + 49 Reorder the terms: 49 + 14x + x2 = -38 + 49 Combine like terms: -38 + 49 = 11 49 + 14x + x2 = 11 Factor a perfect square on the left side: (x + 7)(x + 7) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 7) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 7 = 3.31662479 Simplifying x + 7 = 3.31662479 Reorder the terms: 7 + x = 3.31662479 Solving 7 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 3.31662479 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.31662479 + -7 x = 3.31662479 + -7 Combine like terms: 3.31662479 + -7 = -3.68337521 x = -3.68337521 Simplifying x = -3.68337521Subproblem 2
x + 7 = -3.31662479 Simplifying x + 7 = -3.31662479 Reorder the terms: 7 + x = -3.31662479 Solving 7 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -3.31662479 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.31662479 + -7 x = -3.31662479 + -7 Combine like terms: -3.31662479 + -7 = -10.31662479 x = -10.31662479 Simplifying x = -10.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.68337521, -10.31662479}
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