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Simplifying 16.12 = -0.5x2 + 0.5x + 28 Reorder the terms: 16.12 = 28 + 0.5x + -0.5x2 Solving 16.12 = 28 + 0.5x + -0.5x2 Solving for variable 'x'. Combine like terms: 16.12 + -28 = -11.88 -11.88 + -0.5x + 0.5x2 = 28 + 0.5x + -0.5x2 + -28 + -0.5x + 0.5x2 Reorder the terms: -11.88 + -0.5x + 0.5x2 = 28 + -28 + 0.5x + -0.5x + -0.5x2 + 0.5x2 Combine like terms: 28 + -28 = 0 -11.88 + -0.5x + 0.5x2 = 0 + 0.5x + -0.5x + -0.5x2 + 0.5x2 -11.88 + -0.5x + 0.5x2 = 0.5x + -0.5x + -0.5x2 + 0.5x2 Combine like terms: 0.5x + -0.5x = 0.0 -11.88 + -0.5x + 0.5x2 = 0.0 + -0.5x2 + 0.5x2 -11.88 + -0.5x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -11.88 + -0.5x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -23.76 + -1x + x2 = 0 Move the constant term to the right: Add '23.76' to each side of the equation. -23.76 + -1x + 23.76 + x2 = 0 + 23.76 Reorder the terms: -23.76 + 23.76 + -1x + x2 = 0 + 23.76 Combine like terms: -23.76 + 23.76 = 0.00 0.00 + -1x + x2 = 0 + 23.76 -1x + x2 = 0 + 23.76 Combine like terms: 0 + 23.76 = 23.76 -1x + x2 = 23.76 The x term is -1x. 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. -1x + 0.25 + x2 = 23.76 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 23.76 + 0.25 Combine like terms: 23.76 + 0.25 = 24.01 0.25 + -1x + x2 = 24.01 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 24.01 Calculate the square root of the right side: 4.9 Break this problem into two subproblems by setting (x + -0.5) equal to 4.9 and -4.9.Subproblem 1
x + -0.5 = 4.9 Simplifying x + -0.5 = 4.9 Reorder the terms: -0.5 + x = 4.9 Solving -0.5 + x = 4.9 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 = 4.9 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.9 + 0.5 x = 4.9 + 0.5 Combine like terms: 4.9 + 0.5 = 5.4 x = 5.4 Simplifying x = 5.4Subproblem 2
x + -0.5 = -4.9 Simplifying x + -0.5 = -4.9 Reorder the terms: -0.5 + x = -4.9 Solving -0.5 + x = -4.9 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 = -4.9 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.9 + 0.5 x = -4.9 + 0.5 Combine like terms: -4.9 + 0.5 = -4.4 x = -4.4 Simplifying x = -4.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4, -4.4}
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