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Simplifying 212.5 = 0.5(x + -8)(x) Reorder the terms: 212.5 = 0.5(-8 + x)(x) Reorder the terms for easier multiplication: 212.5 = 0.5x(-8 + x) 212.5 = (-8 * 0.5x + x * 0.5x) 212.5 = (-4x + 0.5x2) Solving 212.5 = -4x + 0.5x2 Solving for variable 'x'. Reorder the terms: 212.5 + 4x + -0.5x2 = -4x + 4x + 0.5x2 + -0.5x2 Combine like terms: -4x + 4x = 0 212.5 + 4x + -0.5x2 = 0 + 0.5x2 + -0.5x2 212.5 + 4x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 212.5 + 4x + -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'. -425 + -8x + x2 = 0 Move the constant term to the right: Add '425' to each side of the equation. -425 + -8x + 425 + x2 = 0 + 425 Reorder the terms: -425 + 425 + -8x + x2 = 0 + 425 Combine like terms: -425 + 425 = 0 0 + -8x + x2 = 0 + 425 -8x + x2 = 0 + 425 Combine like terms: 0 + 425 = 425 -8x + x2 = 425 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 425 + 16 Reorder the terms: 16 + -8x + x2 = 425 + 16 Combine like terms: 425 + 16 = 441 16 + -8x + x2 = 441 Factor a perfect square on the left side: (x + -4)(x + -4) = 441 Calculate the square root of the right side: 21 Break this problem into two subproblems by setting (x + -4) equal to 21 and -21.Subproblem 1
x + -4 = 21 Simplifying x + -4 = 21 Reorder the terms: -4 + x = 21 Solving -4 + x = 21 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 21 + 4 Combine like terms: -4 + 4 = 0 0 + x = 21 + 4 x = 21 + 4 Combine like terms: 21 + 4 = 25 x = 25 Simplifying x = 25Subproblem 2
x + -4 = -21 Simplifying x + -4 = -21 Reorder the terms: -4 + x = -21 Solving -4 + x = -21 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -21 + 4 Combine like terms: -4 + 4 = 0 0 + x = -21 + 4 x = -21 + 4 Combine like terms: -21 + 4 = -17 x = -17 Simplifying x = -17Solution
The solution to the problem is based on the solutions from the subproblems. x = {25, -17}
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