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Simplifying 16 + -0.25x2 = 2x + 4 Reorder the terms: 16 + -0.25x2 = 4 + 2x Solving 16 + -0.25x2 = 4 + 2x Solving for variable 'x'. Reorder the terms: 16 + -4 + -2x + -0.25x2 = 4 + 2x + -4 + -2x Combine like terms: 16 + -4 = 12 12 + -2x + -0.25x2 = 4 + 2x + -4 + -2x Reorder the terms: 12 + -2x + -0.25x2 = 4 + -4 + 2x + -2x Combine like terms: 4 + -4 = 0 12 + -2x + -0.25x2 = 0 + 2x + -2x 12 + -2x + -0.25x2 = 2x + -2x Combine like terms: 2x + -2x = 0 12 + -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'. -48 + 8x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 8x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 8x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 8x + x2 = 0 + 48 8x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 8x + x2 = 48 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 = 48 + 16 Reorder the terms: 16 + 8x + x2 = 48 + 16 Combine like terms: 48 + 16 = 64 16 + 8x + x2 = 64 Factor a perfect square on the left side: (x + 4)(x + 4) = 64 Calculate the square root of the right side: 8 Break this problem into two subproblems by setting (x + 4) equal to 8 and -8.Subproblem 1
x + 4 = 8 Simplifying x + 4 = 8 Reorder the terms: 4 + x = 8 Solving 4 + x = 8 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 = 8 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8 + -4 x = 8 + -4 Combine like terms: 8 + -4 = 4 x = 4 Simplifying x = 4Subproblem 2
x + 4 = -8 Simplifying x + 4 = -8 Reorder the terms: 4 + x = -8 Solving 4 + x = -8 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 = -8 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8 + -4 x = -8 + -4 Combine like terms: -8 + -4 = -12 x = -12 Simplifying x = -12Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -12}
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