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Simplifying (x + -7)(x + -7) = 6 Reorder the terms: (-7 + x)(x + -7) = 6 Reorder the terms: (-7 + x)(-7 + x) = 6 Multiply (-7 + x) * (-7 + x) (-7(-7 + x) + x(-7 + x)) = 6 ((-7 * -7 + x * -7) + x(-7 + x)) = 6 ((49 + -7x) + x(-7 + x)) = 6 (49 + -7x + (-7 * x + x * x)) = 6 (49 + -7x + (-7x + x2)) = 6 Combine like terms: -7x + -7x = -14x (49 + -14x + x2) = 6 Solving 49 + -14x + x2 = 6 Solving for variable 'x'. Reorder the terms: 49 + -6 + -14x + x2 = 6 + -6 Combine like terms: 49 + -6 = 43 43 + -14x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 43 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + -14x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + -14x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -14x + x2 = 0 + -43 -14x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 -14x + x2 = -43 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 = -43 + 49 Reorder the terms: 49 + -14x + x2 = -43 + 49 Combine like terms: -43 + 49 = 6 49 + -14x + x2 = 6 Factor a perfect square on the left side: (x + -7)(x + -7) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -7) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -7 = 2.449489743 Simplifying x + -7 = 2.449489743 Reorder the terms: -7 + x = 2.449489743 Solving -7 + x = 2.449489743 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 = 2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + x = 2.449489743 + 7 x = 2.449489743 + 7 Combine like terms: 2.449489743 + 7 = 9.449489743 x = 9.449489743 Simplifying x = 9.449489743Subproblem 2
x + -7 = -2.449489743 Simplifying x + -7 = -2.449489743 Reorder the terms: -7 + x = -2.449489743 Solving -7 + x = -2.449489743 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 = -2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + x = -2.449489743 + 7 x = -2.449489743 + 7 Combine like terms: -2.449489743 + 7 = 4.550510257 x = 4.550510257 Simplifying x = 4.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.449489743, 4.550510257}
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