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Simplifying -16x2 + 30x + 6 = 10 Reorder the terms: 6 + 30x + -16x2 = 10 Solving 6 + 30x + -16x2 = 10 Solving for variable 'x'. Reorder the terms: 6 + -10 + 30x + -16x2 = 10 + -10 Combine like terms: 6 + -10 = -4 -4 + 30x + -16x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -4 + 30x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 15x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 15x + -8x2)' equal to zero and attempt to solve: Simplifying -2 + 15x + -8x2 = 0 Solving -2 + 15x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.25 + -1.875x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.875x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.875x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.875x + x2 = 0 + -0.25 -1.875x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.875x + x2 = -0.25 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 = -0.25 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = -0.25 + 0.87890625 Combine like terms: -0.25 + 0.87890625 = 0.62890625 0.87890625 + -1.875x + x2 = 0.62890625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 0.62890625 Calculate the square root of the right side: 0.793036096 Break this problem into two subproblems by setting (x + -0.9375) equal to 0.793036096 and -0.793036096.Subproblem 1
x + -0.9375 = 0.793036096 Simplifying x + -0.9375 = 0.793036096 Reorder the terms: -0.9375 + x = 0.793036096 Solving -0.9375 + x = 0.793036096 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 = 0.793036096 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 0.793036096 + 0.9375 x = 0.793036096 + 0.9375 Combine like terms: 0.793036096 + 0.9375 = 1.730536096 x = 1.730536096 Simplifying x = 1.730536096Subproblem 2
x + -0.9375 = -0.793036096 Simplifying x + -0.9375 = -0.793036096 Reorder the terms: -0.9375 + x = -0.793036096 Solving -0.9375 + x = -0.793036096 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 = -0.793036096 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -0.793036096 + 0.9375 x = -0.793036096 + 0.9375 Combine like terms: -0.793036096 + 0.9375 = 0.144463904 x = 0.144463904 Simplifying x = 0.144463904Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.730536096, 0.144463904}Solution
x = {1.730536096, 0.144463904}
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