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Simplifying -16x2 + -32x + 48 = 3 Reorder the terms: 48 + -32x + -16x2 = 3 Solving 48 + -32x + -16x2 = 3 Solving for variable 'x'. Reorder the terms: 48 + -3 + -32x + -16x2 = 3 + -3 Combine like terms: 48 + -3 = 45 45 + -32x + -16x2 = 3 + -3 Combine like terms: 3 + -3 = 0 45 + -32x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.8125 + 2x + x2 = 0 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + 2x + 2.8125 + x2 = 0 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + 2x + x2 = 0 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + 2x + x2 = 0 + 2.8125 2x + x2 = 0 + 2.8125 Combine like terms: 0 + 2.8125 = 2.8125 2x + x2 = 2.8125 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 = 2.8125 + 1 Reorder the terms: 1 + 2x + x2 = 2.8125 + 1 Combine like terms: 2.8125 + 1 = 3.8125 1 + 2x + x2 = 3.8125 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (x + 1) equal to 1.952562419 and -1.952562419.Subproblem 1
x + 1 = 1.952562419 Simplifying x + 1 = 1.952562419 Reorder the terms: 1 + x = 1.952562419 Solving 1 + x = 1.952562419 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 = 1.952562419 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.952562419 + -1 x = 1.952562419 + -1 Combine like terms: 1.952562419 + -1 = 0.952562419 x = 0.952562419 Simplifying x = 0.952562419Subproblem 2
x + 1 = -1.952562419 Simplifying x + 1 = -1.952562419 Reorder the terms: 1 + x = -1.952562419 Solving 1 + x = -1.952562419 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 = -1.952562419 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.952562419 + -1 x = -1.952562419 + -1 Combine like terms: -1.952562419 + -1 = -2.952562419 x = -2.952562419 Simplifying x = -2.952562419Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.952562419, -2.952562419}
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