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Simplifying 0 = x2 + 48x + 398 Reorder the terms: 0 = 398 + 48x + x2 Solving 0 = 398 + 48x + x2 Solving for variable 'x'. Combine like terms: 0 + -398 = -398 -398 + -48x + -1x2 = 398 + 48x + x2 + -398 + -48x + -1x2 Reorder the terms: -398 + -48x + -1x2 = 398 + -398 + 48x + -48x + x2 + -1x2 Combine like terms: 398 + -398 = 0 -398 + -48x + -1x2 = 0 + 48x + -48x + x2 + -1x2 -398 + -48x + -1x2 = 48x + -48x + x2 + -1x2 Combine like terms: 48x + -48x = 0 -398 + -48x + -1x2 = 0 + x2 + -1x2 -398 + -48x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -398 + -48x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(398 + 48x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(398 + 48x + x2)' equal to zero and attempt to solve: Simplifying 398 + 48x + x2 = 0 Solving 398 + 48x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-398' to each side of the equation. 398 + 48x + -398 + x2 = 0 + -398 Reorder the terms: 398 + -398 + 48x + x2 = 0 + -398 Combine like terms: 398 + -398 = 0 0 + 48x + x2 = 0 + -398 48x + x2 = 0 + -398 Combine like terms: 0 + -398 = -398 48x + x2 = -398 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 = -398 + 576 Reorder the terms: 576 + 48x + x2 = -398 + 576 Combine like terms: -398 + 576 = 178 576 + 48x + x2 = 178 Factor a perfect square on the left side: (x + 24)(x + 24) = 178 Calculate the square root of the right side: 13.341664064 Break this problem into two subproblems by setting (x + 24) equal to 13.341664064 and -13.341664064.Subproblem 1
x + 24 = 13.341664064 Simplifying x + 24 = 13.341664064 Reorder the terms: 24 + x = 13.341664064 Solving 24 + x = 13.341664064 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 = 13.341664064 + -24 Combine like terms: 24 + -24 = 0 0 + x = 13.341664064 + -24 x = 13.341664064 + -24 Combine like terms: 13.341664064 + -24 = -10.658335936 x = -10.658335936 Simplifying x = -10.658335936Subproblem 2
x + 24 = -13.341664064 Simplifying x + 24 = -13.341664064 Reorder the terms: 24 + x = -13.341664064 Solving 24 + x = -13.341664064 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 = -13.341664064 + -24 Combine like terms: 24 + -24 = 0 0 + x = -13.341664064 + -24 x = -13.341664064 + -24 Combine like terms: -13.341664064 + -24 = -37.341664064 x = -37.341664064 Simplifying x = -37.341664064Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.658335936, -37.341664064}Solution
x = {-10.658335936, -37.341664064}
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