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Simplifying (4x + 8) * 4x + -16 = 3 Reorder the terms: (8 + 4x) * 4x + -16 = 3 Reorder the terms for easier multiplication: 4x(8 + 4x) + -16 = 3 (8 * 4x + 4x * 4x) + -16 = 3 (32x + 16x2) + -16 = 3 Reorder the terms: -16 + 32x + 16x2 = 3 Solving -16 + 32x + 16x2 = 3 Solving for variable 'x'. Reorder the terms: -16 + -3 + 32x + 16x2 = 3 + -3 Combine like terms: -16 + -3 = -19 -19 + 32x + 16x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -19 + 32x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.1875 + 2x + x2 = 0 Move the constant term to the right: Add '1.1875' to each side of the equation. -1.1875 + 2x + 1.1875 + x2 = 0 + 1.1875 Reorder the terms: -1.1875 + 1.1875 + 2x + x2 = 0 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + 2x + x2 = 0 + 1.1875 2x + x2 = 0 + 1.1875 Combine like terms: 0 + 1.1875 = 1.1875 2x + x2 = 1.1875 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.1875 + 1 Reorder the terms: 1 + 2x + x2 = 1.1875 + 1 Combine like terms: 1.1875 + 1 = 2.1875 1 + 2x + x2 = 2.1875 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.1875 Calculate the square root of the right side: 1.479019946 Break this problem into two subproblems by setting (x + 1) equal to 1.479019946 and -1.479019946.Subproblem 1
x + 1 = 1.479019946 Simplifying x + 1 = 1.479019946 Reorder the terms: 1 + x = 1.479019946 Solving 1 + x = 1.479019946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.479019946 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.479019946 + -1 x = 1.479019946 + -1 Combine like terms: 1.479019946 + -1 = 0.479019946 x = 0.479019946 Simplifying x = 0.479019946Subproblem 2
x + 1 = -1.479019946 Simplifying x + 1 = -1.479019946 Reorder the terms: 1 + x = -1.479019946 Solving 1 + x = -1.479019946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.479019946 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.479019946 + -1 x = -1.479019946 + -1 Combine like terms: -1.479019946 + -1 = -2.479019946 x = -2.479019946 Simplifying x = -2.479019946Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.479019946, -2.479019946}
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