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Simplifying -25x2 + 19x + 16 = 0 Reorder the terms: 16 + 19x + -25x2 = 0 Solving 16 + 19x + -25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.64 + -0.76x + x2 = 0 Move the constant term to the right: Add '0.64' to each side of the equation. -0.64 + -0.76x + 0.64 + x2 = 0 + 0.64 Reorder the terms: -0.64 + 0.64 + -0.76x + x2 = 0 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + -0.76x + x2 = 0 + 0.64 -0.76x + x2 = 0 + 0.64 Combine like terms: 0 + 0.64 = 0.64 -0.76x + x2 = 0.64 The x term is -0.76x. Take half its coefficient (-0.38). Square it (0.1444) and add it to both sides. Add '0.1444' to each side of the equation. -0.76x + 0.1444 + x2 = 0.64 + 0.1444 Reorder the terms: 0.1444 + -0.76x + x2 = 0.64 + 0.1444 Combine like terms: 0.64 + 0.1444 = 0.7844 0.1444 + -0.76x + x2 = 0.7844 Factor a perfect square on the left side: (x + -0.38)(x + -0.38) = 0.7844 Calculate the square root of the right side: 0.885663593 Break this problem into two subproblems by setting (x + -0.38) equal to 0.885663593 and -0.885663593.Subproblem 1
x + -0.38 = 0.885663593 Simplifying x + -0.38 = 0.885663593 Reorder the terms: -0.38 + x = 0.885663593 Solving -0.38 + x = 0.885663593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.38' to each side of the equation. -0.38 + 0.38 + x = 0.885663593 + 0.38 Combine like terms: -0.38 + 0.38 = 0.00 0.00 + x = 0.885663593 + 0.38 x = 0.885663593 + 0.38 Combine like terms: 0.885663593 + 0.38 = 1.265663593 x = 1.265663593 Simplifying x = 1.265663593Subproblem 2
x + -0.38 = -0.885663593 Simplifying x + -0.38 = -0.885663593 Reorder the terms: -0.38 + x = -0.885663593 Solving -0.38 + x = -0.885663593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.38' to each side of the equation. -0.38 + 0.38 + x = -0.885663593 + 0.38 Combine like terms: -0.38 + 0.38 = 0.00 0.00 + x = -0.885663593 + 0.38 x = -0.885663593 + 0.38 Combine like terms: -0.885663593 + 0.38 = -0.505663593 x = -0.505663593 Simplifying x = -0.505663593Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.265663593, -0.505663593}
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