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Simplifying (x + -7)(x + -7) = 60 Reorder the terms: (-7 + x)(x + -7) = 60 Reorder the terms: (-7 + x)(-7 + x) = 60 Multiply (-7 + x) * (-7 + x) (-7(-7 + x) + x(-7 + x)) = 60 ((-7 * -7 + x * -7) + x(-7 + x)) = 60 ((49 + -7x) + x(-7 + x)) = 60 (49 + -7x + (-7 * x + x * x)) = 60 (49 + -7x + (-7x + x2)) = 60 Combine like terms: -7x + -7x = -14x (49 + -14x + x2) = 60 Solving 49 + -14x + x2 = 60 Solving for variable 'x'. Reorder the terms: 49 + -60 + -14x + x2 = 60 + -60 Combine like terms: 49 + -60 = -11 -11 + -14x + x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -11 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -14x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -14x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -14x + x2 = 0 + 11 -14x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -14x + x2 = 11 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 = 11 + 49 Reorder the terms: 49 + -14x + x2 = 11 + 49 Combine like terms: 11 + 49 = 60 49 + -14x + x2 = 60 Factor a perfect square on the left side: (x + -7)(x + -7) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -7) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -7 = 7.745966692 Simplifying x + -7 = 7.745966692 Reorder the terms: -7 + x = 7.745966692 Solving -7 + x = 7.745966692 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 = 7.745966692 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.745966692 + 7 x = 7.745966692 + 7 Combine like terms: 7.745966692 + 7 = 14.745966692 x = 14.745966692 Simplifying x = 14.745966692Subproblem 2
x + -7 = -7.745966692 Simplifying x + -7 = -7.745966692 Reorder the terms: -7 + x = -7.745966692 Solving -7 + x = -7.745966692 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 = -7.745966692 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.745966692 + 7 x = -7.745966692 + 7 Combine like terms: -7.745966692 + 7 = -0.745966692 x = -0.745966692 Simplifying x = -0.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.745966692, -0.745966692}
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