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Simplifying (x + -7)(x + -7) = 14x Reorder the terms: (-7 + x)(x + -7) = 14x Reorder the terms: (-7 + x)(-7 + x) = 14x Multiply (-7 + x) * (-7 + x) (-7(-7 + x) + x(-7 + x)) = 14x ((-7 * -7 + x * -7) + x(-7 + x)) = 14x ((49 + -7x) + x(-7 + x)) = 14x (49 + -7x + (-7 * x + x * x)) = 14x (49 + -7x + (-7x + x2)) = 14x Combine like terms: -7x + -7x = -14x (49 + -14x + x2) = 14x Solving 49 + -14x + x2 = 14x Solving for variable 'x'. Reorder the terms: 49 + -14x + -14x + x2 = 14x + -14x Combine like terms: -14x + -14x = -28x 49 + -28x + x2 = 14x + -14x Combine like terms: 14x + -14x = 0 49 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -28x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -28x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -28x + x2 = 0 + -49 -28x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -28x + x2 = -49 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -49 + 196 Reorder the terms: 196 + -28x + x2 = -49 + 196 Combine like terms: -49 + 196 = 147 196 + -28x + x2 = 147 Factor a perfect square on the left side: (x + -14)(x + -14) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (x + -14) equal to 12.124355653 and -12.124355653.Subproblem 1
x + -14 = 12.124355653 Simplifying x + -14 = 12.124355653 Reorder the terms: -14 + x = 12.124355653 Solving -14 + x = 12.124355653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 12.124355653 + 14 Combine like terms: -14 + 14 = 0 0 + x = 12.124355653 + 14 x = 12.124355653 + 14 Combine like terms: 12.124355653 + 14 = 26.124355653 x = 26.124355653 Simplifying x = 26.124355653Subproblem 2
x + -14 = -12.124355653 Simplifying x + -14 = -12.124355653 Reorder the terms: -14 + x = -12.124355653 Solving -14 + x = -12.124355653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -12.124355653 + 14 Combine like terms: -14 + 14 = 0 0 + x = -12.124355653 + 14 x = -12.124355653 + 14 Combine like terms: -12.124355653 + 14 = 1.875644347 x = 1.875644347 Simplifying x = 1.875644347Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.124355653, 1.875644347}
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