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Simplifying 4x2 + -27x + -53 = 0 Reorder the terms: -53 + -27x + 4x2 = 0 Solving -53 + -27x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.25 + -6.75x + x2 = 0 Move the constant term to the right: Add '13.25' to each side of the equation. -13.25 + -6.75x + 13.25 + x2 = 0 + 13.25 Reorder the terms: -13.25 + 13.25 + -6.75x + x2 = 0 + 13.25 Combine like terms: -13.25 + 13.25 = 0.00 0.00 + -6.75x + x2 = 0 + 13.25 -6.75x + x2 = 0 + 13.25 Combine like terms: 0 + 13.25 = 13.25 -6.75x + x2 = 13.25 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = 13.25 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = 13.25 + 11.390625 Combine like terms: 13.25 + 11.390625 = 24.640625 11.390625 + -6.75x + x2 = 24.640625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 24.640625 Calculate the square root of the right side: 4.963932413 Break this problem into two subproblems by setting (x + -3.375) equal to 4.963932413 and -4.963932413.Subproblem 1
x + -3.375 = 4.963932413 Simplifying x + -3.375 = 4.963932413 Reorder the terms: -3.375 + x = 4.963932413 Solving -3.375 + x = 4.963932413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 4.963932413 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 4.963932413 + 3.375 x = 4.963932413 + 3.375 Combine like terms: 4.963932413 + 3.375 = 8.338932413 x = 8.338932413 Simplifying x = 8.338932413Subproblem 2
x + -3.375 = -4.963932413 Simplifying x + -3.375 = -4.963932413 Reorder the terms: -3.375 + x = -4.963932413 Solving -3.375 + x = -4.963932413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -4.963932413 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -4.963932413 + 3.375 x = -4.963932413 + 3.375 Combine like terms: -4.963932413 + 3.375 = -1.588932413 x = -1.588932413 Simplifying x = -1.588932413Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.338932413, -1.588932413}
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