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Simplifying -16x2 + 30x + 225 = 0 Reorder the terms: 225 + 30x + -16x2 = 0 Solving 225 + 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'. -14.0625 + -1.875x + x2 = 0 Move the constant term to the right: Add '14.0625' to each side of the equation. -14.0625 + -1.875x + 14.0625 + x2 = 0 + 14.0625 Reorder the terms: -14.0625 + 14.0625 + -1.875x + x2 = 0 + 14.0625 Combine like terms: -14.0625 + 14.0625 = 0.0000 0.0000 + -1.875x + x2 = 0 + 14.0625 -1.875x + x2 = 0 + 14.0625 Combine like terms: 0 + 14.0625 = 14.0625 -1.875x + x2 = 14.0625 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 = 14.0625 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 14.0625 + 0.87890625 Combine like terms: 14.0625 + 0.87890625 = 14.94140625 0.87890625 + -1.875x + x2 = 14.94140625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 14.94140625 Calculate the square root of the right side: 3.865411524 Break this problem into two subproblems by setting (x + -0.9375) equal to 3.865411524 and -3.865411524.Subproblem 1
x + -0.9375 = 3.865411524 Simplifying x + -0.9375 = 3.865411524 Reorder the terms: -0.9375 + x = 3.865411524 Solving -0.9375 + x = 3.865411524 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 = 3.865411524 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 3.865411524 + 0.9375 x = 3.865411524 + 0.9375 Combine like terms: 3.865411524 + 0.9375 = 4.802911524 x = 4.802911524 Simplifying x = 4.802911524Subproblem 2
x + -0.9375 = -3.865411524 Simplifying x + -0.9375 = -3.865411524 Reorder the terms: -0.9375 + x = -3.865411524 Solving -0.9375 + x = -3.865411524 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 = -3.865411524 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -3.865411524 + 0.9375 x = -3.865411524 + 0.9375 Combine like terms: -3.865411524 + 0.9375 = -2.927911524 x = -2.927911524 Simplifying x = -2.927911524Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.802911524, -2.927911524}
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