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Simplifying -16x2 + 38.8x + 3 = 0 Reorder the terms: 3 + 38.8x + -16x2 = 0 Solving 3 + 38.8x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.1875 + -2.425x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -2.425x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -2.425x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -2.425x + x2 = 0 + 0.1875 -2.425x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -2.425x + x2 = 0.1875 The x term is -2.425x. Take half its coefficient (-1.2125). Square it (1.47015625) and add it to both sides. Add '1.47015625' to each side of the equation. -2.425x + 1.47015625 + x2 = 0.1875 + 1.47015625 Reorder the terms: 1.47015625 + -2.425x + x2 = 0.1875 + 1.47015625 Combine like terms: 0.1875 + 1.47015625 = 1.65765625 1.47015625 + -2.425x + x2 = 1.65765625 Factor a perfect square on the left side: (x + -1.2125)(x + -1.2125) = 1.65765625 Calculate the square root of the right side: 1.2875 Break this problem into two subproblems by setting (x + -1.2125) equal to 1.2875 and -1.2875.Subproblem 1
x + -1.2125 = 1.2875 Simplifying x + -1.2125 = 1.2875 Reorder the terms: -1.2125 + x = 1.2875 Solving -1.2125 + x = 1.2875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2125' to each side of the equation. -1.2125 + 1.2125 + x = 1.2875 + 1.2125 Combine like terms: -1.2125 + 1.2125 = 0.0000 0.0000 + x = 1.2875 + 1.2125 x = 1.2875 + 1.2125 Combine like terms: 1.2875 + 1.2125 = 2.5 x = 2.5 Simplifying x = 2.5Subproblem 2
x + -1.2125 = -1.2875 Simplifying x + -1.2125 = -1.2875 Reorder the terms: -1.2125 + x = -1.2875 Solving -1.2125 + x = -1.2875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2125' to each side of the equation. -1.2125 + 1.2125 + x = -1.2875 + 1.2125 Combine like terms: -1.2125 + 1.2125 = 0.0000 0.0000 + x = -1.2875 + 1.2125 x = -1.2875 + 1.2125 Combine like terms: -1.2875 + 1.2125 = -0.075 x = -0.075 Simplifying x = -0.075Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5, -0.075}
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