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Simplifying x2 + -96x + 144 = 0 Reorder the terms: 144 + -96x + x2 = 0 Solving 144 + -96x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + -96x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + -96x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -96x + x2 = 0 + -144 -96x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 -96x + x2 = -144 The x term is -96x. Take half its coefficient (-48). Square it (2304) and add it to both sides. Add '2304' to each side of the equation. -96x + 2304 + x2 = -144 + 2304 Reorder the terms: 2304 + -96x + x2 = -144 + 2304 Combine like terms: -144 + 2304 = 2160 2304 + -96x + x2 = 2160 Factor a perfect square on the left side: (x + -48)(x + -48) = 2160 Calculate the square root of the right side: 46.475800154 Break this problem into two subproblems by setting (x + -48) equal to 46.475800154 and -46.475800154.Subproblem 1
x + -48 = 46.475800154 Simplifying x + -48 = 46.475800154 Reorder the terms: -48 + x = 46.475800154 Solving -48 + x = 46.475800154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = 46.475800154 + 48 Combine like terms: -48 + 48 = 0 0 + x = 46.475800154 + 48 x = 46.475800154 + 48 Combine like terms: 46.475800154 + 48 = 94.475800154 x = 94.475800154 Simplifying x = 94.475800154Subproblem 2
x + -48 = -46.475800154 Simplifying x + -48 = -46.475800154 Reorder the terms: -48 + x = -46.475800154 Solving -48 + x = -46.475800154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = -46.475800154 + 48 Combine like terms: -48 + 48 = 0 0 + x = -46.475800154 + 48 x = -46.475800154 + 48 Combine like terms: -46.475800154 + 48 = 1.524199846 x = 1.524199846 Simplifying x = 1.524199846Solution
The solution to the problem is based on the solutions from the subproblems. x = {94.475800154, 1.524199846}
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