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Simplifying (x + 24)(x + 24) = 7 Reorder the terms: (24 + x)(x + 24) = 7 Reorder the terms: (24 + x)(24 + x) = 7 Multiply (24 + x) * (24 + x) (24(24 + x) + x(24 + x)) = 7 ((24 * 24 + x * 24) + x(24 + x)) = 7 ((576 + 24x) + x(24 + x)) = 7 (576 + 24x + (24 * x + x * x)) = 7 (576 + 24x + (24x + x2)) = 7 Combine like terms: 24x + 24x = 48x (576 + 48x + x2) = 7 Solving 576 + 48x + x2 = 7 Solving for variable 'x'. Reorder the terms: 576 + -7 + 48x + x2 = 7 + -7 Combine like terms: 576 + -7 = 569 569 + 48x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 569 + 48x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-569' to each side of the equation. 569 + 48x + -569 + x2 = 0 + -569 Reorder the terms: 569 + -569 + 48x + x2 = 0 + -569 Combine like terms: 569 + -569 = 0 0 + 48x + x2 = 0 + -569 48x + x2 = 0 + -569 Combine like terms: 0 + -569 = -569 48x + x2 = -569 The x term is 48x. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48x + 576 + x2 = -569 + 576 Reorder the terms: 576 + 48x + x2 = -569 + 576 Combine like terms: -569 + 576 = 7 576 + 48x + x2 = 7 Factor a perfect square on the left side: (x + 24)(x + 24) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 24) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 24 = 2.645751311 Simplifying x + 24 = 2.645751311 Reorder the terms: 24 + x = 2.645751311 Solving 24 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 2.645751311 + -24 Combine like terms: 24 + -24 = 0 0 + x = 2.645751311 + -24 x = 2.645751311 + -24 Combine like terms: 2.645751311 + -24 = -21.354248689 x = -21.354248689 Simplifying x = -21.354248689Subproblem 2
x + 24 = -2.645751311 Simplifying x + 24 = -2.645751311 Reorder the terms: 24 + x = -2.645751311 Solving 24 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -2.645751311 + -24 Combine like terms: 24 + -24 = 0 0 + x = -2.645751311 + -24 x = -2.645751311 + -24 Combine like terms: -2.645751311 + -24 = -26.645751311 x = -26.645751311 Simplifying x = -26.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-21.354248689, -26.645751311}
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