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Simplifying -16x2 + 10x + 5.5 = 0 Reorder the terms: 5.5 + 10x + -16x2 = 0 Solving 5.5 + 10x + -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'. -0.34375 + -0.625x + x2 = 0 Move the constant term to the right: Add '0.34375' to each side of the equation. -0.34375 + -0.625x + 0.34375 + x2 = 0 + 0.34375 Reorder the terms: -0.34375 + 0.34375 + -0.625x + x2 = 0 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + -0.625x + x2 = 0 + 0.34375 -0.625x + x2 = 0 + 0.34375 Combine like terms: 0 + 0.34375 = 0.34375 -0.625x + x2 = 0.34375 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 0.34375 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 0.34375 + 0.09765625 Combine like terms: 0.34375 + 0.09765625 = 0.44140625 0.09765625 + -0.625x + x2 = 0.44140625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 0.44140625 Calculate the square root of the right side: 0.664384113 Break this problem into two subproblems by setting (x + -0.3125) equal to 0.664384113 and -0.664384113.Subproblem 1
x + -0.3125 = 0.664384113 Simplifying x + -0.3125 = 0.664384113 Reorder the terms: -0.3125 + x = 0.664384113 Solving -0.3125 + x = 0.664384113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 0.664384113 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 0.664384113 + 0.3125 x = 0.664384113 + 0.3125 Combine like terms: 0.664384113 + 0.3125 = 0.976884113 x = 0.976884113 Simplifying x = 0.976884113Subproblem 2
x + -0.3125 = -0.664384113 Simplifying x + -0.3125 = -0.664384113 Reorder the terms: -0.3125 + x = -0.664384113 Solving -0.3125 + x = -0.664384113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -0.664384113 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -0.664384113 + 0.3125 x = -0.664384113 + 0.3125 Combine like terms: -0.664384113 + 0.3125 = -0.351884113 x = -0.351884113 Simplifying x = -0.351884113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.976884113, -0.351884113}
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