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Simplifying 16x2 + -14x + -3 = 0 Reorder the terms: -3 + -14x + 16x2 = 0 Solving -3 + -14x + 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 + -0.875x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -0.875x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -0.875x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -0.875x + x2 = 0 + 0.1875 -0.875x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -0.875x + x2 = 0.1875 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 0.1875 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 0.1875 + 0.19140625 Combine like terms: 0.1875 + 0.19140625 = 0.37890625 0.19140625 + -0.875x + x2 = 0.37890625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 0.37890625 Calculate the square root of the right side: 0.615553613 Break this problem into two subproblems by setting (x + -0.4375) equal to 0.615553613 and -0.615553613.Subproblem 1
x + -0.4375 = 0.615553613 Simplifying x + -0.4375 = 0.615553613 Reorder the terms: -0.4375 + x = 0.615553613 Solving -0.4375 + x = 0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 0.615553613 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 0.615553613 + 0.4375 x = 0.615553613 + 0.4375 Combine like terms: 0.615553613 + 0.4375 = 1.053053613 x = 1.053053613 Simplifying x = 1.053053613Subproblem 2
x + -0.4375 = -0.615553613 Simplifying x + -0.4375 = -0.615553613 Reorder the terms: -0.4375 + x = -0.615553613 Solving -0.4375 + x = -0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -0.615553613 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -0.615553613 + 0.4375 x = -0.615553613 + 0.4375 Combine like terms: -0.615553613 + 0.4375 = -0.178053613 x = -0.178053613 Simplifying x = -0.178053613Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.053053613, -0.178053613}
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