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Simplifying 5x2 + -19x + 16 = 0 Reorder the terms: 16 + -19x + 5x2 = 0 Solving 16 + -19x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + -3.8x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -3.8x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -3.8x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -3.8x + x2 = 0 + -3.2 -3.8x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -3.8x + x2 = -3.2 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = -3.2 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = -3.2 + 3.61 Combine like terms: -3.2 + 3.61 = 0.41 3.61 + -3.8x + x2 = 0.41 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + -1.9) equal to 0.640312424 and -0.640312424.Subproblem 1
x + -1.9 = 0.640312424 Simplifying x + -1.9 = 0.640312424 Reorder the terms: -1.9 + x = 0.640312424 Solving -1.9 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 0.640312424 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 0.640312424 + 1.9 x = 0.640312424 + 1.9 Combine like terms: 0.640312424 + 1.9 = 2.540312424 x = 2.540312424 Simplifying x = 2.540312424Subproblem 2
x + -1.9 = -0.640312424 Simplifying x + -1.9 = -0.640312424 Reorder the terms: -1.9 + x = -0.640312424 Solving -1.9 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -0.640312424 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -0.640312424 + 1.9 x = -0.640312424 + 1.9 Combine like terms: -0.640312424 + 1.9 = 1.259687576 x = 1.259687576 Simplifying x = 1.259687576Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.540312424, 1.259687576}
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