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Simplifying 0 = -16x2 + 30x + 6 Reorder the terms: 0 = 6 + 30x + -16x2 Solving 0 = 6 + 30x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -30x + 16x2 = 6 + 30x + -16x2 + -6 + -30x + 16x2 Reorder the terms: -6 + -30x + 16x2 = 6 + -6 + 30x + -30x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -6 + -30x + 16x2 = 0 + 30x + -30x + -16x2 + 16x2 -6 + -30x + 16x2 = 30x + -30x + -16x2 + 16x2 Combine like terms: 30x + -30x = 0 -6 + -30x + 16x2 = 0 + -16x2 + 16x2 -6 + -30x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6 + -30x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -15x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -15x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -15x + 8x2 = 0 Solving -3 + -15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -1.875x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -1.875x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -1.875x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -1.875x + x2 = 0 + 0.375 -1.875x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -1.875x + x2 = 0.375 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 = 0.375 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 0.375 + 0.87890625 Combine like terms: 0.375 + 0.87890625 = 1.25390625 0.87890625 + -1.875x + x2 = 1.25390625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 1.25390625 Calculate the square root of the right side: 1.119779554 Break this problem into two subproblems by setting (x + -0.9375) equal to 1.119779554 and -1.119779554.Subproblem 1
x + -0.9375 = 1.119779554 Simplifying x + -0.9375 = 1.119779554 Reorder the terms: -0.9375 + x = 1.119779554 Solving -0.9375 + x = 1.119779554 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 = 1.119779554 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 1.119779554 + 0.9375 x = 1.119779554 + 0.9375 Combine like terms: 1.119779554 + 0.9375 = 2.057279554 x = 2.057279554 Simplifying x = 2.057279554Subproblem 2
x + -0.9375 = -1.119779554 Simplifying x + -0.9375 = -1.119779554 Reorder the terms: -0.9375 + x = -1.119779554 Solving -0.9375 + x = -1.119779554 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 = -1.119779554 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -1.119779554 + 0.9375 x = -1.119779554 + 0.9375 Combine like terms: -1.119779554 + 0.9375 = -0.182279554 x = -0.182279554 Simplifying x = -0.182279554Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.057279554, -0.182279554}Solution
x = {2.057279554, -0.182279554}
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