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Simplifying (x + 7)(x + 7) = 19 Reorder the terms: (7 + x)(x + 7) = 19 Reorder the terms: (7 + x)(7 + x) = 19 Multiply (7 + x) * (7 + x) (7(7 + x) + x(7 + x)) = 19 ((7 * 7 + x * 7) + x(7 + x)) = 19 ((49 + 7x) + x(7 + x)) = 19 (49 + 7x + (7 * x + x * x)) = 19 (49 + 7x + (7x + x2)) = 19 Combine like terms: 7x + 7x = 14x (49 + 14x + x2) = 19 Solving 49 + 14x + x2 = 19 Solving for variable 'x'. Reorder the terms: 49 + -19 + 14x + x2 = 19 + -19 Combine like terms: 49 + -19 = 30 30 + 14x + x2 = 19 + -19 Combine like terms: 19 + -19 = 0 30 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 14x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 14x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 14x + x2 = 0 + -30 14x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 14x + x2 = -30 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 = -30 + 49 Reorder the terms: 49 + 14x + x2 = -30 + 49 Combine like terms: -30 + 49 = 19 49 + 14x + x2 = 19 Factor a perfect square on the left side: (x + 7)(x + 7) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 7) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 7 = 4.358898944 Simplifying x + 7 = 4.358898944 Reorder the terms: 7 + x = 4.358898944 Solving 7 + x = 4.358898944 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 = 4.358898944 + -7 Combine like terms: 7 + -7 = 0 0 + x = 4.358898944 + -7 x = 4.358898944 + -7 Combine like terms: 4.358898944 + -7 = -2.641101056 x = -2.641101056 Simplifying x = -2.641101056Subproblem 2
x + 7 = -4.358898944 Simplifying x + 7 = -4.358898944 Reorder the terms: 7 + x = -4.358898944 Solving 7 + x = -4.358898944 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 = -4.358898944 + -7 Combine like terms: 7 + -7 = 0 0 + x = -4.358898944 + -7 x = -4.358898944 + -7 Combine like terms: -4.358898944 + -7 = -11.358898944 x = -11.358898944 Simplifying x = -11.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.641101056, -11.358898944}
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