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Simplifying 80.5 = x2 + 3x + 9.5 Reorder the terms: 80.5 = 9.5 + 3x + x2 Solving 80.5 = 9.5 + 3x + x2 Solving for variable 'x'. Combine like terms: 80.5 + -9.5 = 71 71 + -3x + -1x2 = 9.5 + 3x + x2 + -9.5 + -3x + -1x2 Reorder the terms: 71 + -3x + -1x2 = 9.5 + -9.5 + 3x + -3x + x2 + -1x2 Combine like terms: 9.5 + -9.5 = 0.0 71 + -3x + -1x2 = 0.0 + 3x + -3x + x2 + -1x2 71 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 71 + -3x + -1x2 = 0 + x2 + -1x2 71 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 71 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -71 + 3x + x2 = 0 Move the constant term to the right: Add '71' to each side of the equation. -71 + 3x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + 3x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 3x + x2 = 0 + 71 3x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 3x + x2 = 71 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 71 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 71 + 2.25 Combine like terms: 71 + 2.25 = 73.25 2.25 + 3x + x2 = 73.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 73.25 Calculate the square root of the right side: 8.558621384 Break this problem into two subproblems by setting (x + 1.5) equal to 8.558621384 and -8.558621384.Subproblem 1
x + 1.5 = 8.558621384 Simplifying x + 1.5 = 8.558621384 Reorder the terms: 1.5 + x = 8.558621384 Solving 1.5 + x = 8.558621384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 8.558621384 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.558621384 + -1.5 x = 8.558621384 + -1.5 Combine like terms: 8.558621384 + -1.5 = 7.058621384 x = 7.058621384 Simplifying x = 7.058621384Subproblem 2
x + 1.5 = -8.558621384 Simplifying x + 1.5 = -8.558621384 Reorder the terms: 1.5 + x = -8.558621384 Solving 1.5 + x = -8.558621384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -8.558621384 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.558621384 + -1.5 x = -8.558621384 + -1.5 Combine like terms: -8.558621384 + -1.5 = -10.058621384 x = -10.058621384 Simplifying x = -10.058621384Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.058621384, -10.058621384}
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