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Simplifying 82.8 = 0.8x2 + -24x + 250 Reorder the terms: 82.8 = 250 + -24x + 0.8x2 Solving 82.8 = 250 + -24x + 0.8x2 Solving for variable 'x'. Combine like terms: 82.8 + -250 = -167.2 -167.2 + 24x + -0.8x2 = 250 + -24x + 0.8x2 + -250 + 24x + -0.8x2 Reorder the terms: -167.2 + 24x + -0.8x2 = 250 + -250 + -24x + 24x + 0.8x2 + -0.8x2 Combine like terms: 250 + -250 = 0 -167.2 + 24x + -0.8x2 = 0 + -24x + 24x + 0.8x2 + -0.8x2 -167.2 + 24x + -0.8x2 = -24x + 24x + 0.8x2 + -0.8x2 Combine like terms: -24x + 24x = 0 -167.2 + 24x + -0.8x2 = 0 + 0.8x2 + -0.8x2 -167.2 + 24x + -0.8x2 = 0.8x2 + -0.8x2 Combine like terms: 0.8x2 + -0.8x2 = 0.0 -167.2 + 24x + -0.8x2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 209 + -30x + x2 = 0 Move the constant term to the right: Add '-209' to each side of the equation. 209 + -30x + -209 + x2 = 0 + -209 Reorder the terms: 209 + -209 + -30x + x2 = 0 + -209 Combine like terms: 209 + -209 = 0 0 + -30x + x2 = 0 + -209 -30x + x2 = 0 + -209 Combine like terms: 0 + -209 = -209 -30x + x2 = -209 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -209 + 225 Reorder the terms: 225 + -30x + x2 = -209 + 225 Combine like terms: -209 + 225 = 16 225 + -30x + x2 = 16 Factor a perfect square on the left side: (x + -15)(x + -15) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -15) equal to 4 and -4.Subproblem 1
x + -15 = 4 Simplifying x + -15 = 4 Reorder the terms: -15 + x = 4 Solving -15 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 4 + 15 Combine like terms: -15 + 15 = 0 0 + x = 4 + 15 x = 4 + 15 Combine like terms: 4 + 15 = 19 x = 19 Simplifying x = 19Subproblem 2
x + -15 = -4 Simplifying x + -15 = -4 Reorder the terms: -15 + x = -4 Solving -15 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -4 + 15 Combine like terms: -15 + 15 = 0 0 + x = -4 + 15 x = -4 + 15 Combine like terms: -4 + 15 = 11 x = 11 Simplifying x = 11Solution
The solution to the problem is based on the solutions from the subproblems. x = {19, 11}
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