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Simplifying (0.5x2) + -1(10x) + (32) = 0 Remove parenthesis around (10x) (0.5x2) + -1 * 10x + (32) = 0 Multiply -1 * 10 (0.5x2) + -10x + (32) = 0 (0.5x2) + -10x + 32 = 0 Reorder the terms: 32 + -10x + (0.5x2) = 0 Solving 32 + -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'. 64 + -20x + x2 = 0 Move the constant term to the right: Add '-64' to each side of the equation. 64 + -20x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -20x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -20x + x2 = 0 + -64 -20x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -20x + x2 = -64 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 = -64 + 100 Reorder the terms: 100 + -20x + x2 = -64 + 100 Combine like terms: -64 + 100 = 36 100 + -20x + x2 = 36 Factor a perfect square on the left side: ((x) + -10)((x) + -10) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting ((x) + -10) equal to 6 and -6.Subproblem 1
(x) + -10 = 6 Simplifying (x) + -10 = 6 x + -10 = 6 Reorder the terms: -10 + x = 6 Solving -10 + x = 6 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 = 6 + 10 Combine like terms: -10 + 10 = 0 0 + x = 6 + 10 x = 6 + 10 Combine like terms: 6 + 10 = 16 x = 16 Simplifying x = 16Subproblem 2
(x) + -10 = -6 Simplifying (x) + -10 = -6 x + -10 = -6 Reorder the terms: -10 + x = -6 Solving -10 + x = -6 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 = -6 + 10 Combine like terms: -10 + 10 = 0 0 + x = -6 + 10 x = -6 + 10 Combine like terms: -6 + 10 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {16, 4}
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