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Simplifying 16x2 + -19x + -12 = 0 Reorder the terms: -12 + -19x + 16x2 = 0 Solving -12 + -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'. -0.75 + -1.1875x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.1875x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.1875x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.1875x + x2 = 0 + 0.75 -1.1875x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.1875x + x2 = 0.75 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 = 0.75 + 0.3525390625 Reorder the terms: 0.3525390625 + -1.1875x + x2 = 0.75 + 0.3525390625 Combine like terms: 0.75 + 0.3525390625 = 1.1025390625 0.3525390625 + -1.1875x + x2 = 1.1025390625 Factor a perfect square on the left side: (x + -0.59375)(x + -0.59375) = 1.1025390625 Calculate the square root of the right side: 1.050018601 Break this problem into two subproblems by setting (x + -0.59375) equal to 1.050018601 and -1.050018601.Subproblem 1
x + -0.59375 = 1.050018601 Simplifying x + -0.59375 = 1.050018601 Reorder the terms: -0.59375 + x = 1.050018601 Solving -0.59375 + x = 1.050018601 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 = 1.050018601 + 0.59375 Combine like terms: -0.59375 + 0.59375 = 0.00000 0.00000 + x = 1.050018601 + 0.59375 x = 1.050018601 + 0.59375 Combine like terms: 1.050018601 + 0.59375 = 1.643768601 x = 1.643768601 Simplifying x = 1.643768601Subproblem 2
x + -0.59375 = -1.050018601 Simplifying x + -0.59375 = -1.050018601 Reorder the terms: -0.59375 + x = -1.050018601 Solving -0.59375 + x = -1.050018601 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 = -1.050018601 + 0.59375 Combine like terms: -0.59375 + 0.59375 = 0.00000 0.00000 + x = -1.050018601 + 0.59375 x = -1.050018601 + 0.59375 Combine like terms: -1.050018601 + 0.59375 = -0.456268601 x = -0.456268601 Simplifying x = -0.456268601Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.643768601, -0.456268601}
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