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Simplifying 4x2 + 16x + -4.25 = 0 Reorder the terms: -4.25 + 16x + 4x2 = 0 Solving -4.25 + 16x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.0625 + 4x + x2 = 0 Move the constant term to the right: Add '1.0625' to each side of the equation. -1.0625 + 4x + 1.0625 + x2 = 0 + 1.0625 Reorder the terms: -1.0625 + 1.0625 + 4x + x2 = 0 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + 4x + x2 = 0 + 1.0625 4x + x2 = 0 + 1.0625 Combine like terms: 0 + 1.0625 = 1.0625 4x + x2 = 1.0625 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.0625 + 4 Reorder the terms: 4 + 4x + x2 = 1.0625 + 4 Combine like terms: 1.0625 + 4 = 5.0625 4 + 4x + x2 = 5.0625 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + 2) equal to 2.25 and -2.25.Subproblem 1
x + 2 = 2.25 Simplifying x + 2 = 2.25 Reorder the terms: 2 + x = 2.25 Solving 2 + x = 2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.25 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.25 + -2 x = 2.25 + -2 Combine like terms: 2.25 + -2 = 0.25 x = 0.25 Simplifying x = 0.25Subproblem 2
x + 2 = -2.25 Simplifying x + 2 = -2.25 Reorder the terms: 2 + x = -2.25 Solving 2 + x = -2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.25 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.25 + -2 x = -2.25 + -2 Combine like terms: -2.25 + -2 = -4.25 x = -4.25 Simplifying x = -4.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.25, -4.25}
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