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Simplifying (x + -7)(x + -7) = 98 Reorder the terms: (-7 + x)(x + -7) = 98 Reorder the terms: (-7 + x)(-7 + x) = 98 Multiply (-7 + x) * (-7 + x) (-7(-7 + x) + x(-7 + x)) = 98 ((-7 * -7 + x * -7) + x(-7 + x)) = 98 ((49 + -7x) + x(-7 + x)) = 98 (49 + -7x + (-7 * x + x * x)) = 98 (49 + -7x + (-7x + x2)) = 98 Combine like terms: -7x + -7x = -14x (49 + -14x + x2) = 98 Solving 49 + -14x + x2 = 98 Solving for variable 'x'. Reorder the terms: 49 + -98 + -14x + x2 = 98 + -98 Combine like terms: 49 + -98 = -49 -49 + -14x + x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -49 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -14x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -14x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -14x + x2 = 0 + 49 -14x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -14x + x2 = 49 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 = 49 + 49 Reorder the terms: 49 + -14x + x2 = 49 + 49 Combine like terms: 49 + 49 = 98 49 + -14x + x2 = 98 Factor a perfect square on the left side: (x + -7)(x + -7) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + -7) equal to 9.899494937 and -9.899494937.Subproblem 1
x + -7 = 9.899494937 Simplifying x + -7 = 9.899494937 Reorder the terms: -7 + x = 9.899494937 Solving -7 + x = 9.899494937 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 = 9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.899494937 + 7 x = 9.899494937 + 7 Combine like terms: 9.899494937 + 7 = 16.899494937 x = 16.899494937 Simplifying x = 16.899494937Subproblem 2
x + -7 = -9.899494937 Simplifying x + -7 = -9.899494937 Reorder the terms: -7 + x = -9.899494937 Solving -7 + x = -9.899494937 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 = -9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.899494937 + 7 x = -9.899494937 + 7 Combine like terms: -9.899494937 + 7 = -2.899494937 x = -2.899494937 Simplifying x = -2.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.899494937, -2.899494937}
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