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Simplifying (0.5x2) + (10x) + -1(8) = 0 Multiply -1 * 8 (0.5x2) + (10x) + -8 = 0 Reorder the terms: -8 + (10x) + (0.5x2) = 0 Solving -8 + (10x) + (0.5x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -16 + (20x) + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + (20x) + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + (20x) + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + (20x) + x2 = 0 + 16 (20x) + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 (20x) + x2 = 16 The x term is (20x). Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. (20x) + 100 + x2 = 16 + 100 Reorder the terms: 100 + (20x) + x2 = 16 + 100 Combine like terms: 16 + 100 = 116 100 + (20x) + x2 = 116 Factor a perfect square on the left side: ((x) + 10)((x) + 10) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting ((x) + 10) equal to 10.770329614 and -10.770329614.Subproblem 1
(x) + 10 = 10.770329614 Simplifying (x) + 10 = 10.770329614 x + 10 = 10.770329614 Reorder the terms: 10 + x = 10.770329614 Solving 10 + x = 10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 10.770329614 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.770329614 + -10 x = 10.770329614 + -10 Combine like terms: 10.770329614 + -10 = 0.770329614 x = 0.770329614 Simplifying x = 0.770329614Subproblem 2
(x) + 10 = -10.770329614 Simplifying (x) + 10 = -10.770329614 x + 10 = -10.770329614 Reorder the terms: 10 + x = -10.770329614 Solving 10 + x = -10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -10.770329614 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.770329614 + -10 x = -10.770329614 + -10 Combine like terms: -10.770329614 + -10 = -20.770329614 x = -20.770329614 Simplifying x = -20.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.770329614, -20.770329614}
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