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Simplifying 4x2 + -19x + -96 = 0 Reorder the terms: -96 + -19x + 4x2 = 0 Solving -96 + -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'. -24 + -4.75x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -4.75x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -4.75x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -4.75x + x2 = 0 + 24 -4.75x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -4.75x + x2 = 24 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 = 24 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 24 + 5.640625 Combine like terms: 24 + 5.640625 = 29.640625 5.640625 + -4.75x + x2 = 29.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 29.640625 Calculate the square root of the right side: 5.444320435 Break this problem into two subproblems by setting (x + -2.375) equal to 5.444320435 and -5.444320435.Subproblem 1
x + -2.375 = 5.444320435 Simplifying x + -2.375 = 5.444320435 Reorder the terms: -2.375 + x = 5.444320435 Solving -2.375 + x = 5.444320435 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 = 5.444320435 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 5.444320435 + 2.375 x = 5.444320435 + 2.375 Combine like terms: 5.444320435 + 2.375 = 7.819320435 x = 7.819320435 Simplifying x = 7.819320435Subproblem 2
x + -2.375 = -5.444320435 Simplifying x + -2.375 = -5.444320435 Reorder the terms: -2.375 + x = -5.444320435 Solving -2.375 + x = -5.444320435 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 = -5.444320435 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -5.444320435 + 2.375 x = -5.444320435 + 2.375 Combine like terms: -5.444320435 + 2.375 = -3.069320435 x = -3.069320435 Simplifying x = -3.069320435Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.819320435, -3.069320435}
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