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Simplifying x2 + 48x + 100 = 0 Reorder the terms: 100 + 48x + x2 = 0 Solving 100 + 48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + 48x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 48x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 48x + x2 = 0 + -100 48x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 48x + x2 = -100 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 = -100 + 576 Reorder the terms: 576 + 48x + x2 = -100 + 576 Combine like terms: -100 + 576 = 476 576 + 48x + x2 = 476 Factor a perfect square on the left side: (x + 24)(x + 24) = 476 Calculate the square root of the right side: 21.817424229 Break this problem into two subproblems by setting (x + 24) equal to 21.817424229 and -21.817424229.Subproblem 1
x + 24 = 21.817424229 Simplifying x + 24 = 21.817424229 Reorder the terms: 24 + x = 21.817424229 Solving 24 + x = 21.817424229 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 = 21.817424229 + -24 Combine like terms: 24 + -24 = 0 0 + x = 21.817424229 + -24 x = 21.817424229 + -24 Combine like terms: 21.817424229 + -24 = -2.182575771 x = -2.182575771 Simplifying x = -2.182575771Subproblem 2
x + 24 = -21.817424229 Simplifying x + 24 = -21.817424229 Reorder the terms: 24 + x = -21.817424229 Solving 24 + x = -21.817424229 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 = -21.817424229 + -24 Combine like terms: 24 + -24 = 0 0 + x = -21.817424229 + -24 x = -21.817424229 + -24 Combine like terms: -21.817424229 + -24 = -45.817424229 x = -45.817424229 Simplifying x = -45.817424229Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.182575771, -45.817424229}
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