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Simplifying 5x2 + -16x + -97 = 0 Reorder the terms: -97 + -16x + 5x2 = 0 Solving -97 + -16x + 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'. -19.4 + -3.2x + x2 = 0 Move the constant term to the right: Add '19.4' to each side of the equation. -19.4 + -3.2x + 19.4 + x2 = 0 + 19.4 Reorder the terms: -19.4 + 19.4 + -3.2x + x2 = 0 + 19.4 Combine like terms: -19.4 + 19.4 = 0.0 0.0 + -3.2x + x2 = 0 + 19.4 -3.2x + x2 = 0 + 19.4 Combine like terms: 0 + 19.4 = 19.4 -3.2x + x2 = 19.4 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 19.4 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 19.4 + 2.56 Combine like terms: 19.4 + 2.56 = 21.96 2.56 + -3.2x + x2 = 21.96 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 21.96 Calculate the square root of the right side: 4.686149806 Break this problem into two subproblems by setting (x + -1.6) equal to 4.686149806 and -4.686149806.Subproblem 1
x + -1.6 = 4.686149806 Simplifying x + -1.6 = 4.686149806 Reorder the terms: -1.6 + x = 4.686149806 Solving -1.6 + x = 4.686149806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 4.686149806 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 4.686149806 + 1.6 x = 4.686149806 + 1.6 Combine like terms: 4.686149806 + 1.6 = 6.286149806 x = 6.286149806 Simplifying x = 6.286149806Subproblem 2
x + -1.6 = -4.686149806 Simplifying x + -1.6 = -4.686149806 Reorder the terms: -1.6 + x = -4.686149806 Solving -1.6 + x = -4.686149806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -4.686149806 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -4.686149806 + 1.6 x = -4.686149806 + 1.6 Combine like terms: -4.686149806 + 1.6 = -3.086149806 x = -3.086149806 Simplifying x = -3.086149806Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.286149806, -3.086149806}
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