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Simplifying 16 = (x + 0.5)(x + 0.5) Reorder the terms: 16 = (0.5 + x)(x + 0.5) Reorder the terms: 16 = (0.5 + x)(0.5 + x) Multiply (0.5 + x) * (0.5 + x) 16 = (0.5(0.5 + x) + x(0.5 + x)) 16 = ((0.5 * 0.5 + x * 0.5) + x(0.5 + x)) 16 = ((0.25 + 0.5x) + x(0.5 + x)) 16 = (0.25 + 0.5x + (0.5 * x + x * x)) 16 = (0.25 + 0.5x + (0.5x + x2)) Combine like terms: 0.5x + 0.5x = 1x 16 = (0.25 + 1x + x2) Solving 16 = 0.25 + 1x + x2 Solving for variable 'x'. Combine like terms: 16 + -0.25 = 15.75 15.75 + -1x + -1x2 = 0.25 + 1x + x2 + -0.25 + -1x + -1x2 Reorder the terms: 15.75 + -1x + -1x2 = 0.25 + -0.25 + 1x + -1x + x2 + -1x2 Combine like terms: 0.25 + -0.25 = 0.00 15.75 + -1x + -1x2 = 0.00 + 1x + -1x + x2 + -1x2 15.75 + -1x + -1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 15.75 + -1x + -1x2 = 0 + x2 + -1x2 15.75 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15.75 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15.75 + x + x2 = 0 Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + x + 15.75 + x2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + x + x2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + x + x2 = 0 + 15.75 x + x2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 x + x2 = 15.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 15.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 15.75 + 0.25 Combine like terms: 15.75 + 0.25 = 16 1.25 + x2 = 16 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + 0.5) equal to 4 and -4.Subproblem 1
x + 0.5 = 4 Simplifying x + 0.5 = 4 Reorder the terms: 0.5 + x = 4 Solving 0.5 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4 + -0.5 x = 4 + -0.5 Combine like terms: 4 + -0.5 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + 0.5 = -4 Simplifying x + 0.5 = -4 Reorder the terms: 0.5 + x = -4 Solving 0.5 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4 + -0.5 x = -4 + -0.5 Combine like terms: -4 + -0.5 = -4.5 x = -4.5 Simplifying x = -4.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, -4.5}
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