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Simplifying 2x2 + -7.5x + x2 = 8.5 Reorder the terms: -7.5x + 2x2 + x2 = 8.5 Combine like terms: 2x2 + x2 = 3x2 -7.5x + 3x2 = 8.5 Solving -7.5x + 3x2 = 8.5 Solving for variable 'x'. Reorder the terms: -8.5 + -7.5x + 3x2 = 8.5 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 -8.5 + -7.5x + 3x2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.833333333 + -2.5x + x2 = 0.0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + -2.5x + 2.833333333 + x2 = 0.0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + -2.5x + x2 = 0.0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + -2.5x + x2 = 0.0 + 2.833333333 -2.5x + x2 = 0.0 + 2.833333333 Combine like terms: 0.0 + 2.833333333 = 2.833333333 -2.5x + x2 = 2.833333333 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 2.833333333 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 2.833333333 + 1.5625 Combine like terms: 2.833333333 + 1.5625 = 4.395833333 1.5625 + -2.5x + x2 = 4.395833333 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 4.395833333 Calculate the square root of the right side: 2.096624271 Break this problem into two subproblems by setting (x + -1.25) equal to 2.096624271 and -2.096624271.Subproblem 1
x + -1.25 = 2.096624271 Simplifying x + -1.25 = 2.096624271 Reorder the terms: -1.25 + x = 2.096624271 Solving -1.25 + x = 2.096624271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.096624271 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.096624271 + 1.25 x = 2.096624271 + 1.25 Combine like terms: 2.096624271 + 1.25 = 3.346624271 x = 3.346624271 Simplifying x = 3.346624271Subproblem 2
x + -1.25 = -2.096624271 Simplifying x + -1.25 = -2.096624271 Reorder the terms: -1.25 + x = -2.096624271 Solving -1.25 + x = -2.096624271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.096624271 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.096624271 + 1.25 x = -2.096624271 + 1.25 Combine like terms: -2.096624271 + 1.25 = -0.846624271 x = -0.846624271 Simplifying x = -0.846624271Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.346624271, -0.846624271}
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