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Simplifying 0.5x2 + 6x + 10.5 = 2 Reorder the terms: 10.5 + 6x + 0.5x2 = 2 Solving 10.5 + 6x + 0.5x2 = 2 Solving for variable 'x'. Reorder the terms: 10.5 + -2 + 6x + 0.5x2 = 2 + -2 Combine like terms: 10.5 + -2 = 8.5 8.5 + 6x + 0.5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 8.5 + 6x + 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 + 12x + x2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + 12x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 12x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 12x + x2 = 0 + -17 12x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 12x + x2 = -17 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -17 + 36 Reorder the terms: 36 + 12x + x2 = -17 + 36 Combine like terms: -17 + 36 = 19 36 + 12x + x2 = 19 Factor a perfect square on the left side: (x + 6)(x + 6) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 6) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 6 = 4.358898944 Simplifying x + 6 = 4.358898944 Reorder the terms: 6 + x = 4.358898944 Solving 6 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 4.358898944 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.358898944 + -6 x = 4.358898944 + -6 Combine like terms: 4.358898944 + -6 = -1.641101056 x = -1.641101056 Simplifying x = -1.641101056Subproblem 2
x + 6 = -4.358898944 Simplifying x + 6 = -4.358898944 Reorder the terms: 6 + x = -4.358898944 Solving 6 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -4.358898944 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.358898944 + -6 x = -4.358898944 + -6 Combine like terms: -4.358898944 + -6 = -10.358898944 x = -10.358898944 Simplifying x = -10.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.641101056, -10.358898944}
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