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Simplifying 0 = 0.25x2 + x + -15 Reorder the terms: 0 = -15 + x + 0.25x2 Solving 0 = -15 + x + 0.25x2 Solving for variable 'x'. Combine like terms: 0 + 15 = 15 15 + -1x + -0.25x2 = -15 + x + 0.25x2 + 15 + -1x + -0.25x2 Reorder the terms: 15 + -1x + -0.25x2 = -15 + 15 + x + -1x + 0.25x2 + -0.25x2 Combine like terms: -15 + 15 = 0 15 + -1x + -0.25x2 = 0 + x + -1x + 0.25x2 + -0.25x2 15 + -1x + -0.25x2 = x + -1x + 0.25x2 + -0.25x2 Combine like terms: x + -1x = 0 15 + -1x + -0.25x2 = 0 + 0.25x2 + -0.25x2 15 + -1x + -0.25x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 15 + -1x + -0.25x2 = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -60 + 4x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 4x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 4x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 4x + x2 = 0 + 60 4x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 4x + x2 = 60 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 = 60 + 4 Reorder the terms: 4 + 4x + x2 = 60 + 4 Combine like terms: 60 + 4 = 64 4 + 4x + x2 = 64 Factor a perfect square on the left side: (x + 2)(x + 2) = 64 Calculate the square root of the right side: 8 Break this problem into two subproblems by setting (x + 2) equal to 8 and -8.Subproblem 1
x + 2 = 8 Simplifying x + 2 = 8 Reorder the terms: 2 + x = 8 Solving 2 + x = 8 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 = 8 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8 + -2 x = 8 + -2 Combine like terms: 8 + -2 = 6 x = 6 Simplifying x = 6Subproblem 2
x + 2 = -8 Simplifying x + 2 = -8 Reorder the terms: 2 + x = -8 Solving 2 + x = -8 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 = -8 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8 + -2 x = -8 + -2 Combine like terms: -8 + -2 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, -10}
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