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Simplifying 0.5x2 + -5x = 42 Reorder the terms: -5x + 0.5x2 = 42 Solving -5x + 0.5x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + -5x + 0.5x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + -5x + 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'. -84 + -10x + x2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + -10x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -10x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -10x + x2 = 0 + 84 -10x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -10x + x2 = 84 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 84 + 25 Reorder the terms: 25 + -10x + x2 = 84 + 25 Combine like terms: 84 + 25 = 109 25 + -10x + x2 = 109 Factor a perfect square on the left side: (x + -5)(x + -5) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + -5) equal to 10.440306509 and -10.440306509.Subproblem 1
x + -5 = 10.440306509 Simplifying x + -5 = 10.440306509 Reorder the terms: -5 + x = 10.440306509 Solving -5 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 10.440306509 + 5 Combine like terms: -5 + 5 = 0 0 + x = 10.440306509 + 5 x = 10.440306509 + 5 Combine like terms: 10.440306509 + 5 = 15.440306509 x = 15.440306509 Simplifying x = 15.440306509Subproblem 2
x + -5 = -10.440306509 Simplifying x + -5 = -10.440306509 Reorder the terms: -5 + x = -10.440306509 Solving -5 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -10.440306509 + 5 Combine like terms: -5 + 5 = 0 0 + x = -10.440306509 + 5 x = -10.440306509 + 5 Combine like terms: -10.440306509 + 5 = -5.440306509 x = -5.440306509 Simplifying x = -5.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.440306509, -5.440306509}
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