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Simplifying -16x2 + 30x + 3 = 0 Reorder the terms: 3 + 30x + -16x2 = 0 Solving 3 + 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'. -0.1875 + -1.875x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -1.875x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -1.875x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -1.875x + x2 = 0 + 0.1875 -1.875x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -1.875x + x2 = 0.1875 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 = 0.1875 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 0.1875 + 0.87890625 Combine like terms: 0.1875 + 0.87890625 = 1.06640625 0.87890625 + -1.875x + x2 = 1.06640625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 1.06640625 Calculate the square root of the right side: 1.032669478 Break this problem into two subproblems by setting (x + -0.9375) equal to 1.032669478 and -1.032669478.Subproblem 1
x + -0.9375 = 1.032669478 Simplifying x + -0.9375 = 1.032669478 Reorder the terms: -0.9375 + x = 1.032669478 Solving -0.9375 + x = 1.032669478 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 = 1.032669478 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 1.032669478 + 0.9375 x = 1.032669478 + 0.9375 Combine like terms: 1.032669478 + 0.9375 = 1.970169478 x = 1.970169478 Simplifying x = 1.970169478Subproblem 2
x + -0.9375 = -1.032669478 Simplifying x + -0.9375 = -1.032669478 Reorder the terms: -0.9375 + x = -1.032669478 Solving -0.9375 + x = -1.032669478 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 = -1.032669478 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -1.032669478 + 0.9375 x = -1.032669478 + 0.9375 Combine like terms: -1.032669478 + 0.9375 = -0.095169478 x = -0.095169478 Simplifying x = -0.095169478Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.970169478, -0.095169478}
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