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Simplifying 0.16x2 + -2.8x + 1.3 = 0 Reorder the terms: 1.3 + -2.8x + 0.16x2 = 0 Solving 1.3 + -2.8x + 0.16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. 8.125 + -17.5x + x2 = 0 Move the constant term to the right: Add '-8.125' to each side of the equation. 8.125 + -17.5x + -8.125 + x2 = 0 + -8.125 Reorder the terms: 8.125 + -8.125 + -17.5x + x2 = 0 + -8.125 Combine like terms: 8.125 + -8.125 = 0.000 0.000 + -17.5x + x2 = 0 + -8.125 -17.5x + x2 = 0 + -8.125 Combine like terms: 0 + -8.125 = -8.125 -17.5x + x2 = -8.125 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = -8.125 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = -8.125 + 76.5625 Combine like terms: -8.125 + 76.5625 = 68.4375 76.5625 + -17.5x + x2 = 68.4375 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 68.4375 Calculate the square root of the right side: 8.272696054 Break this problem into two subproblems by setting (x + -8.75) equal to 8.272696054 and -8.272696054.Subproblem 1
x + -8.75 = 8.272696054 Simplifying x + -8.75 = 8.272696054 Reorder the terms: -8.75 + x = 8.272696054 Solving -8.75 + x = 8.272696054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 8.272696054 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 8.272696054 + 8.75 x = 8.272696054 + 8.75 Combine like terms: 8.272696054 + 8.75 = 17.022696054 x = 17.022696054 Simplifying x = 17.022696054Subproblem 2
x + -8.75 = -8.272696054 Simplifying x + -8.75 = -8.272696054 Reorder the terms: -8.75 + x = -8.272696054 Solving -8.75 + x = -8.272696054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -8.272696054 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -8.272696054 + 8.75 x = -8.272696054 + 8.75 Combine like terms: -8.272696054 + 8.75 = 0.477303946 x = 0.477303946 Simplifying x = 0.477303946Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.022696054, 0.477303946}
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