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Simplifying -16x2 + 30x + 6.6 = 0 Reorder the terms: 6.6 + 30x + -16x2 = 0 Solving 6.6 + 30x + -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'. -0.4125 + -1.875x + x2 = 0 Move the constant term to the right: Add '0.4125' to each side of the equation. -0.4125 + -1.875x + 0.4125 + x2 = 0 + 0.4125 Reorder the terms: -0.4125 + 0.4125 + -1.875x + x2 = 0 + 0.4125 Combine like terms: -0.4125 + 0.4125 = 0.0000 0.0000 + -1.875x + x2 = 0 + 0.4125 -1.875x + x2 = 0 + 0.4125 Combine like terms: 0 + 0.4125 = 0.4125 -1.875x + x2 = 0.4125 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = 0.4125 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 0.4125 + 0.87890625 Combine like terms: 0.4125 + 0.87890625 = 1.29140625 0.87890625 + -1.875x + x2 = 1.29140625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 1.29140625 Calculate the square root of the right side: 1.136400568 Break this problem into two subproblems by setting (x + -0.9375) equal to 1.136400568 and -1.136400568.Subproblem 1
x + -0.9375 = 1.136400568 Simplifying x + -0.9375 = 1.136400568 Reorder the terms: -0.9375 + x = 1.136400568 Solving -0.9375 + x = 1.136400568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 1.136400568 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 1.136400568 + 0.9375 x = 1.136400568 + 0.9375 Combine like terms: 1.136400568 + 0.9375 = 2.073900568 x = 2.073900568 Simplifying x = 2.073900568Subproblem 2
x + -0.9375 = -1.136400568 Simplifying x + -0.9375 = -1.136400568 Reorder the terms: -0.9375 + x = -1.136400568 Solving -0.9375 + x = -1.136400568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -1.136400568 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -1.136400568 + 0.9375 x = -1.136400568 + 0.9375 Combine like terms: -1.136400568 + 0.9375 = -0.198900568 x = -0.198900568 Simplifying x = -0.198900568Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.073900568, -0.198900568}
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