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Simplifying (x + -7)(x + -7) + -11 = 0 Reorder the terms: (-7 + x)(x + -7) + -11 = 0 Reorder the terms: (-7 + x)(-7 + x) + -11 = 0 Multiply (-7 + x) * (-7 + x) (-7(-7 + x) + x(-7 + x)) + -11 = 0 ((-7 * -7 + x * -7) + x(-7 + x)) + -11 = 0 ((49 + -7x) + x(-7 + x)) + -11 = 0 (49 + -7x + (-7 * x + x * x)) + -11 = 0 (49 + -7x + (-7x + x2)) + -11 = 0 Combine like terms: -7x + -7x = -14x (49 + -14x + x2) + -11 = 0 Reorder the terms: 49 + -11 + -14x + x2 = 0 Combine like terms: 49 + -11 = 38 38 + -14x + x2 = 0 Solving 38 + -14x + x2 = 0 Solving for variable 'x'. 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 = 10.31662479 x = 10.31662479 Simplifying x = 10.31662479Subproblem 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 = 3.68337521 x = 3.68337521 Simplifying x = 3.68337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.31662479, 3.68337521}
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