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Simplifying 0.25x2 + 16 = 2x + 12 Reorder the terms: 16 + 0.25x2 = 2x + 12 Reorder the terms: 16 + 0.25x2 = 12 + 2x Solving 16 + 0.25x2 = 12 + 2x Solving for variable 'x'. Reorder the terms: 16 + -12 + -2x + 0.25x2 = 12 + 2x + -12 + -2x Combine like terms: 16 + -12 = 4 4 + -2x + 0.25x2 = 12 + 2x + -12 + -2x Reorder the terms: 4 + -2x + 0.25x2 = 12 + -12 + 2x + -2x Combine like terms: 12 + -12 = 0 4 + -2x + 0.25x2 = 0 + 2x + -2x 4 + -2x + 0.25x2 = 2x + -2x Combine like terms: 2x + -2x = 0 4 + -2x + 0.25x2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 16 + -8x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -8x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -8x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -8x + x2 = 0 + -16 -8x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -8x + x2 = -16 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -16 + 16 Reorder the terms: 16 + -8x + x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -8x + x2 = 0 Factor a perfect square on the left side: (x + -4)(x + -4) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -4) equal to 0 and 0.Subproblem 1
x + -4 = 0 Simplifying x + -4 = 0 Reorder the terms: -4 + x = 0 Solving -4 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -4 = 0 Simplifying x + -4 = 0 Reorder the terms: -4 + x = 0 Solving -4 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, 4}
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