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Simplifying -16x2 + 30x + 4 = 16 Reorder the terms: 4 + 30x + -16x2 = 16 Solving 4 + 30x + -16x2 = 16 Solving for variable 'x'. Reorder the terms: 4 + -16 + 30x + -16x2 = 16 + -16 Combine like terms: 4 + -16 = -12 -12 + 30x + -16x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -12 + 30x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 15x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 15x + -8x2)' equal to zero and attempt to solve: Simplifying -6 + 15x + -8x2 = 0 Solving -6 + 15x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.75 + -1.875x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -1.875x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -1.875x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -1.875x + x2 = 0 + -0.75 -1.875x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -1.875x + x2 = -0.75 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 = -0.75 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = -0.75 + 0.87890625 Combine like terms: -0.75 + 0.87890625 = 0.12890625 0.87890625 + -1.875x + x2 = 0.12890625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (x + -0.9375) equal to 0.359035165 and -0.359035165.Subproblem 1
x + -0.9375 = 0.359035165 Simplifying x + -0.9375 = 0.359035165 Reorder the terms: -0.9375 + x = 0.359035165 Solving -0.9375 + x = 0.359035165 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 = 0.359035165 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 0.359035165 + 0.9375 x = 0.359035165 + 0.9375 Combine like terms: 0.359035165 + 0.9375 = 1.296535165 x = 1.296535165 Simplifying x = 1.296535165Subproblem 2
x + -0.9375 = -0.359035165 Simplifying x + -0.9375 = -0.359035165 Reorder the terms: -0.9375 + x = -0.359035165 Solving -0.9375 + x = -0.359035165 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 = -0.359035165 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -0.359035165 + 0.9375 x = -0.359035165 + 0.9375 Combine like terms: -0.359035165 + 0.9375 = 0.578464835 x = 0.578464835 Simplifying x = 0.578464835Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.296535165, 0.578464835}Solution
x = {1.296535165, 0.578464835}
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