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Simplifying 2x2 + -19x + 16 = 0 Reorder the terms: 16 + -19x + 2x2 = 0 Solving 16 + -19x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8 + -9.5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -9.5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -9.5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -9.5x + x2 = 0 + -8 -9.5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -9.5x + x2 = -8 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -8 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -8 + 22.5625 Combine like terms: -8 + 22.5625 = 14.5625 22.5625 + -9.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + -4.75) equal to 3.816084381 and -3.816084381.Subproblem 1
x + -4.75 = 3.816084381 Simplifying x + -4.75 = 3.816084381 Reorder the terms: -4.75 + x = 3.816084381 Solving -4.75 + x = 3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 3.816084381 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 3.816084381 + 4.75 x = 3.816084381 + 4.75 Combine like terms: 3.816084381 + 4.75 = 8.566084381 x = 8.566084381 Simplifying x = 8.566084381Subproblem 2
x + -4.75 = -3.816084381 Simplifying x + -4.75 = -3.816084381 Reorder the terms: -4.75 + x = -3.816084381 Solving -4.75 + x = -3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -3.816084381 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -3.816084381 + 4.75 x = -3.816084381 + 4.75 Combine like terms: -3.816084381 + 4.75 = 0.933915619 x = 0.933915619 Simplifying x = 0.933915619Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.566084381, 0.933915619}
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