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Simplifying -0.04x2 + 6.6x + 216 = 278 Reorder the terms: 216 + 6.6x + -0.04x2 = 278 Solving 216 + 6.6x + -0.04x2 = 278 Solving for variable 'x'. Reorder the terms: 216 + -278 + 6.6x + -0.04x2 = 278 + -278 Combine like terms: 216 + -278 = -62 -62 + 6.6x + -0.04x2 = 278 + -278 Combine like terms: 278 + -278 = 0 -62 + 6.6x + -0.04x2 = 0 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. 1550 + -165x + x2 = 0 Move the constant term to the right: Add '-1550' to each side of the equation. 1550 + -165x + -1550 + x2 = 0 + -1550 Reorder the terms: 1550 + -1550 + -165x + x2 = 0 + -1550 Combine like terms: 1550 + -1550 = 0 0 + -165x + x2 = 0 + -1550 -165x + x2 = 0 + -1550 Combine like terms: 0 + -1550 = -1550 -165x + x2 = -1550 The x term is -165x. Take half its coefficient (-82.5). Square it (6806.25) and add it to both sides. Add '6806.25' to each side of the equation. -165x + 6806.25 + x2 = -1550 + 6806.25 Reorder the terms: 6806.25 + -165x + x2 = -1550 + 6806.25 Combine like terms: -1550 + 6806.25 = 5256.25 6806.25 + -165x + x2 = 5256.25 Factor a perfect square on the left side: (x + -82.5)(x + -82.5) = 5256.25 Calculate the square root of the right side: 72.5 Break this problem into two subproblems by setting (x + -82.5) equal to 72.5 and -72.5.Subproblem 1
x + -82.5 = 72.5 Simplifying x + -82.5 = 72.5 Reorder the terms: -82.5 + x = 72.5 Solving -82.5 + x = 72.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '82.5' to each side of the equation. -82.5 + 82.5 + x = 72.5 + 82.5 Combine like terms: -82.5 + 82.5 = 0.0 0.0 + x = 72.5 + 82.5 x = 72.5 + 82.5 Combine like terms: 72.5 + 82.5 = 155 x = 155 Simplifying x = 155Subproblem 2
x + -82.5 = -72.5 Simplifying x + -82.5 = -72.5 Reorder the terms: -82.5 + x = -72.5 Solving -82.5 + x = -72.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '82.5' to each side of the equation. -82.5 + 82.5 + x = -72.5 + 82.5 Combine like terms: -82.5 + 82.5 = 0.0 0.0 + x = -72.5 + 82.5 x = -72.5 + 82.5 Combine like terms: -72.5 + 82.5 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {155, 10}
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