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Simplifying 0.5x2 + 9x + -2.8 = 6 Reorder the terms: -2.8 + 9x + 0.5x2 = 6 Solving -2.8 + 9x + 0.5x2 = 6 Solving for variable 'x'. Reorder the terms: -2.8 + -6 + 9x + 0.5x2 = 6 + -6 Combine like terms: -2.8 + -6 = -8.8 -8.8 + 9x + 0.5x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -8.8 + 9x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -17.6 + 18x + x2 = 0 Move the constant term to the right: Add '17.6' to each side of the equation. -17.6 + 18x + 17.6 + x2 = 0 + 17.6 Reorder the terms: -17.6 + 17.6 + 18x + x2 = 0 + 17.6 Combine like terms: -17.6 + 17.6 = 0.0 0.0 + 18x + x2 = 0 + 17.6 18x + x2 = 0 + 17.6 Combine like terms: 0 + 17.6 = 17.6 18x + x2 = 17.6 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 17.6 + 81 Reorder the terms: 81 + 18x + x2 = 17.6 + 81 Combine like terms: 17.6 + 81 = 98.6 81 + 18x + x2 = 98.6 Factor a perfect square on the left side: (x + 9)(x + 9) = 98.6 Calculate the square root of the right side: 9.92975327 Break this problem into two subproblems by setting (x + 9) equal to 9.92975327 and -9.92975327.Subproblem 1
x + 9 = 9.92975327 Simplifying x + 9 = 9.92975327 Reorder the terms: 9 + x = 9.92975327 Solving 9 + x = 9.92975327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 9.92975327 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.92975327 + -9 x = 9.92975327 + -9 Combine like terms: 9.92975327 + -9 = 0.92975327 x = 0.92975327 Simplifying x = 0.92975327Subproblem 2
x + 9 = -9.92975327 Simplifying x + 9 = -9.92975327 Reorder the terms: 9 + x = -9.92975327 Solving 9 + x = -9.92975327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -9.92975327 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.92975327 + -9 x = -9.92975327 + -9 Combine like terms: -9.92975327 + -9 = -18.92975327 x = -18.92975327 Simplifying x = -18.92975327Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.92975327, -18.92975327}
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