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Simplifying 48 + 96x + -16x2 = 47 Solving 48 + 96x + -16x2 = 47 Solving for variable 'x'. Reorder the terms: 48 + -47 + 96x + -16x2 = 47 + -47 Combine like terms: 48 + -47 = 1 1 + 96x + -16x2 = 47 + -47 Combine like terms: 47 + -47 = 0 1 + 96x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.0625 + -6x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -6x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -6x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -6x + x2 = 0 + 0.0625 -6x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -6x + x2 = 0.0625 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 0.0625 + 9 Reorder the terms: 9 + -6x + x2 = 0.0625 + 9 Combine like terms: 0.0625 + 9 = 9.0625 9 + -6x + x2 = 9.0625 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -3) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -3 = 3.010398645 Simplifying x + -3 = 3.010398645 Reorder the terms: -3 + x = 3.010398645 Solving -3 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.010398645 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.010398645 + 3 x = 3.010398645 + 3 Combine like terms: 3.010398645 + 3 = 6.010398645 x = 6.010398645 Simplifying x = 6.010398645Subproblem 2
x + -3 = -3.010398645 Simplifying x + -3 = -3.010398645 Reorder the terms: -3 + x = -3.010398645 Solving -3 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.010398645 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.010398645 + 3 x = -3.010398645 + 3 Combine like terms: -3.010398645 + 3 = -0.010398645 x = -0.010398645 Simplifying x = -0.010398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.010398645, -0.010398645}
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