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Simplifying 16x2 + 14x + 49 = 52 Reorder the terms: 49 + 14x + 16x2 = 52 Solving 49 + 14x + 16x2 = 52 Solving for variable 'x'. Reorder the terms: 49 + -52 + 14x + 16x2 = 52 + -52 Combine like terms: 49 + -52 = -3 -3 + 14x + 16x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -3 + 14x + 16x2 = 0 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 = 0.178053613 x = 0.178053613 Simplifying x = 0.178053613Subproblem 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 = -1.053053613 x = -1.053053613 Simplifying x = -1.053053613Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.178053613, -1.053053613}
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