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Simplifying x(0.25x) = x + 15 Remove parenthesis around (0.25x) x * 0.25x = x + 15 Reorder the terms for easier multiplication: 0.25x * x = x + 15 Multiply x * x 0.25x2 = x + 15 Reorder the terms: 0.25x2 = 15 + x Solving 0.25x2 = 15 + x Solving for variable 'x'. Reorder the terms: -15 + -1x + 0.25x2 = 15 + x + -15 + -1x Reorder the terms: -15 + -1x + 0.25x2 = 15 + -15 + x + -1x Combine like terms: 15 + -15 = 0 -15 + -1x + 0.25x2 = 0 + x + -1x -15 + -1x + 0.25x2 = x + -1x Combine like terms: x + -1x = 0 -15 + -1x + 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'. -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 = 10 x = 10 Simplifying x = 10Subproblem 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 = -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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