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Simplifying 4x2 + -19x + -52 = 0 Reorder the terms: -52 + -19x + 4x2 = 0 Solving -52 + -19x + 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 + -4.75x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -4.75x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -4.75x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4.75x + x2 = 0 + 13 -4.75x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -4.75x + x2 = 13 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 13 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 13 + 5.640625 Combine like terms: 13 + 5.640625 = 18.640625 5.640625 + -4.75x + x2 = 18.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 18.640625 Calculate the square root of the right side: 4.31747901 Break this problem into two subproblems by setting (x + -2.375) equal to 4.31747901 and -4.31747901.Subproblem 1
x + -2.375 = 4.31747901 Simplifying x + -2.375 = 4.31747901 Reorder the terms: -2.375 + x = 4.31747901 Solving -2.375 + x = 4.31747901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 4.31747901 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 4.31747901 + 2.375 x = 4.31747901 + 2.375 Combine like terms: 4.31747901 + 2.375 = 6.69247901 x = 6.69247901 Simplifying x = 6.69247901Subproblem 2
x + -2.375 = -4.31747901 Simplifying x + -2.375 = -4.31747901 Reorder the terms: -2.375 + x = -4.31747901 Solving -2.375 + x = -4.31747901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -4.31747901 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -4.31747901 + 2.375 x = -4.31747901 + 2.375 Combine like terms: -4.31747901 + 2.375 = -1.94247901 x = -1.94247901 Simplifying x = -1.94247901Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.69247901, -1.94247901}
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