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Simplifying -16x2 + -19x + 120 = 0 Reorder the terms: 120 + -19x + -16x2 = 0 Solving 120 + -19x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -7.5 + 1.1875x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 1.1875x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 1.1875x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 1.1875x + x2 = 0 + 7.5 1.1875x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 1.1875x + x2 = 7.5 The x term is 1.1875x. Take half its coefficient (0.59375). Square it (0.3525390625) and add it to both sides. Add '0.3525390625' to each side of the equation. 1.1875x + 0.3525390625 + x2 = 7.5 + 0.3525390625 Reorder the terms: 0.3525390625 + 1.1875x + x2 = 7.5 + 0.3525390625 Combine like terms: 7.5 + 0.3525390625 = 7.8525390625 0.3525390625 + 1.1875x + x2 = 7.8525390625 Factor a perfect square on the left side: (x + 0.59375)(x + 0.59375) = 7.8525390625 Calculate the square root of the right side: 2.802238224 Break this problem into two subproblems by setting (x + 0.59375) equal to 2.802238224 and -2.802238224.Subproblem 1
x + 0.59375 = 2.802238224 Simplifying x + 0.59375 = 2.802238224 Reorder the terms: 0.59375 + x = 2.802238224 Solving 0.59375 + x = 2.802238224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + x = 2.802238224 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + x = 2.802238224 + -0.59375 x = 2.802238224 + -0.59375 Combine like terms: 2.802238224 + -0.59375 = 2.208488224 x = 2.208488224 Simplifying x = 2.208488224Subproblem 2
x + 0.59375 = -2.802238224 Simplifying x + 0.59375 = -2.802238224 Reorder the terms: 0.59375 + x = -2.802238224 Solving 0.59375 + x = -2.802238224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + x = -2.802238224 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + x = -2.802238224 + -0.59375 x = -2.802238224 + -0.59375 Combine like terms: -2.802238224 + -0.59375 = -3.395988224 x = -3.395988224 Simplifying x = -3.395988224Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.208488224, -3.395988224}
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