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Simplifying 5(x + 7)(x + 7) = 25 Reorder the terms: 5(7 + x)(x + 7) = 25 Reorder the terms: 5(7 + x)(7 + x) = 25 Multiply (7 + x) * (7 + x) 5(7(7 + x) + x(7 + x)) = 25 5((7 * 7 + x * 7) + x(7 + x)) = 25 5((49 + 7x) + x(7 + x)) = 25 5(49 + 7x + (7 * x + x * x)) = 25 5(49 + 7x + (7x + x2)) = 25 Combine like terms: 7x + 7x = 14x 5(49 + 14x + x2) = 25 (49 * 5 + 14x * 5 + x2 * 5) = 25 (245 + 70x + 5x2) = 25 Solving 245 + 70x + 5x2 = 25 Solving for variable 'x'. Reorder the terms: 245 + -25 + 70x + 5x2 = 25 + -25 Combine like terms: 245 + -25 = 220 220 + 70x + 5x2 = 25 + -25 Combine like terms: 25 + -25 = 0 220 + 70x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(44 + 14x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(44 + 14x + x2)' equal to zero and attempt to solve: Simplifying 44 + 14x + x2 = 0 Solving 44 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + 14x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + 14x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + 14x + x2 = 0 + -44 14x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 14x + x2 = -44 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 = -44 + 49 Reorder the terms: 49 + 14x + x2 = -44 + 49 Combine like terms: -44 + 49 = 5 49 + 14x + x2 = 5 Factor a perfect square on the left side: (x + 7)(x + 7) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 7) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 7 = 2.236067978 Simplifying x + 7 = 2.236067978 Reorder the terms: 7 + x = 2.236067978 Solving 7 + x = 2.236067978 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 = 2.236067978 + -7 Combine like terms: 7 + -7 = 0 0 + x = 2.236067978 + -7 x = 2.236067978 + -7 Combine like terms: 2.236067978 + -7 = -4.763932022 x = -4.763932022 Simplifying x = -4.763932022Subproblem 2
x + 7 = -2.236067978 Simplifying x + 7 = -2.236067978 Reorder the terms: 7 + x = -2.236067978 Solving 7 + x = -2.236067978 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 = -2.236067978 + -7 Combine like terms: 7 + -7 = 0 0 + x = -2.236067978 + -7 x = -2.236067978 + -7 Combine like terms: -2.236067978 + -7 = -9.236067978 x = -9.236067978 Simplifying x = -9.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.763932022, -9.236067978}Solution
x = {-4.763932022, -9.236067978}
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