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Simplifying 4x2 + -19x + -360 = 0 Reorder the terms: -360 + -19x + 4x2 = 0 Solving -360 + -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'. -90 + -4.75x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -4.75x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -4.75x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -4.75x + x2 = 0 + 90 -4.75x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -4.75x + x2 = 90 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 = 90 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 90 + 5.640625 Combine like terms: 90 + 5.640625 = 95.640625 5.640625 + -4.75x + x2 = 95.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 95.640625 Calculate the square root of the right side: 9.779602497 Break this problem into two subproblems by setting (x + -2.375) equal to 9.779602497 and -9.779602497.Subproblem 1
x + -2.375 = 9.779602497 Simplifying x + -2.375 = 9.779602497 Reorder the terms: -2.375 + x = 9.779602497 Solving -2.375 + x = 9.779602497 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 = 9.779602497 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 9.779602497 + 2.375 x = 9.779602497 + 2.375 Combine like terms: 9.779602497 + 2.375 = 12.154602497 x = 12.154602497 Simplifying x = 12.154602497Subproblem 2
x + -2.375 = -9.779602497 Simplifying x + -2.375 = -9.779602497 Reorder the terms: -2.375 + x = -9.779602497 Solving -2.375 + x = -9.779602497 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 = -9.779602497 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -9.779602497 + 2.375 x = -9.779602497 + 2.375 Combine like terms: -9.779602497 + 2.375 = -7.404602497 x = -7.404602497 Simplifying x = -7.404602497Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.154602497, -7.404602497}
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