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Simplifying 0.5x2 + -10x + 42 = 0 Reorder the terms: 42 + -10x + 0.5x2 = 0 Solving 42 + -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'. 84 + -20x + x2 = 0 Move the constant term to the right: Add '-84' to each side of the equation. 84 + -20x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + -20x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -20x + x2 = 0 + -84 -20x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 -20x + x2 = -84 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 = -84 + 100 Reorder the terms: 100 + -20x + x2 = -84 + 100 Combine like terms: -84 + 100 = 16 100 + -20x + x2 = 16 Factor a perfect square on the left side: (x + -10)(x + -10) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -10) equal to 4 and -4.Subproblem 1
x + -10 = 4 Simplifying x + -10 = 4 Reorder the terms: -10 + x = 4 Solving -10 + x = 4 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 = 4 + 10 Combine like terms: -10 + 10 = 0 0 + x = 4 + 10 x = 4 + 10 Combine like terms: 4 + 10 = 14 x = 14 Simplifying x = 14Subproblem 2
x + -10 = -4 Simplifying x + -10 = -4 Reorder the terms: -10 + x = -4 Solving -10 + x = -4 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 = -4 + 10 Combine like terms: -10 + 10 = 0 0 + x = -4 + 10 x = -4 + 10 Combine like terms: -4 + 10 = 6 x = 6 Simplifying x = 6Solution
The solution to the problem is based on the solutions from the subproblems. x = {14, 6}
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