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Simplifying (-16x2 + 48x + 3) = 0 Reorder the terms: (3 + 48x + -16x2) = 0 Remove parenthesis around (3 + 48x + -16x2) 3 + 48x + -16x2 = 0 Solving 3 + 48x + -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 + -3x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -3x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -3x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -3x + x2 = 0 + 0.1875 -3x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -3x + x2 = 0.1875 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.1875 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.1875 + 2.25 Combine like terms: 0.1875 + 2.25 = 2.4375 2.25 + -3x + x2 = 2.4375 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.4375 Calculate the square root of the right side: 1.5612495 Break this problem into two subproblems by setting (x + -1.5) equal to 1.5612495 and -1.5612495.Subproblem 1
x + -1.5 = 1.5612495 Simplifying x + -1.5 = 1.5612495 Reorder the terms: -1.5 + x = 1.5612495 Solving -1.5 + x = 1.5612495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.5612495 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.5612495 + 1.5 x = 1.5612495 + 1.5 Combine like terms: 1.5612495 + 1.5 = 3.0612495 x = 3.0612495 Simplifying x = 3.0612495Subproblem 2
x + -1.5 = -1.5612495 Simplifying x + -1.5 = -1.5612495 Reorder the terms: -1.5 + x = -1.5612495 Solving -1.5 + x = -1.5612495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.5612495 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.5612495 + 1.5 x = -1.5612495 + 1.5 Combine like terms: -1.5612495 + 1.5 = -0.0612495 x = -0.0612495 Simplifying x = -0.0612495Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0612495, -0.0612495}
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