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Simplifying 0 = 0.25x2 + -4x + 15 Reorder the terms: 0 = 15 + -4x + 0.25x2 Solving 0 = 15 + -4x + 0.25x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + 4x + -0.25x2 = 15 + -4x + 0.25x2 + -15 + 4x + -0.25x2 Reorder the terms: -15 + 4x + -0.25x2 = 15 + -15 + -4x + 4x + 0.25x2 + -0.25x2 Combine like terms: 15 + -15 = 0 -15 + 4x + -0.25x2 = 0 + -4x + 4x + 0.25x2 + -0.25x2 -15 + 4x + -0.25x2 = -4x + 4x + 0.25x2 + -0.25x2 Combine like terms: -4x + 4x = 0 -15 + 4x + -0.25x2 = 0 + 0.25x2 + -0.25x2 -15 + 4x + -0.25x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 -15 + 4x + -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 + -16x + x2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -16x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -16x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -16x + x2 = 0 + -60 -16x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -16x + x2 = -60 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -60 + 64 Reorder the terms: 64 + -16x + x2 = -60 + 64 Combine like terms: -60 + 64 = 4 64 + -16x + x2 = 4 Factor a perfect square on the left side: (x + -8)(x + -8) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -8) equal to 2 and -2.Subproblem 1
x + -8 = 2 Simplifying x + -8 = 2 Reorder the terms: -8 + x = 2 Solving -8 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 2 + 8 Combine like terms: -8 + 8 = 0 0 + x = 2 + 8 x = 2 + 8 Combine like terms: 2 + 8 = 10 x = 10 Simplifying x = 10Subproblem 2
x + -8 = -2 Simplifying x + -8 = -2 Reorder the terms: -8 + x = -2 Solving -8 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -2 + 8 Combine like terms: -8 + 8 = 0 0 + x = -2 + 8 x = -2 + 8 Combine like terms: -2 + 8 = 6 x = 6 Simplifying x = 6Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, 6}
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