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Simplifying 12 + 10x + 0.5x2 = 762 Solving 12 + 10x + 0.5x2 = 762 Solving for variable 'x'. Reorder the terms: 12 + -762 + 10x + 0.5x2 = 762 + -762 Combine like terms: 12 + -762 = -750 -750 + 10x + 0.5x2 = 762 + -762 Combine like terms: 762 + -762 = 0 -750 + 10x + 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'. -1500 + 20x + x2 = 0 Move the constant term to the right: Add '1500' to each side of the equation. -1500 + 20x + 1500 + x2 = 0 + 1500 Reorder the terms: -1500 + 1500 + 20x + x2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + 20x + x2 = 0 + 1500 20x + x2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 20x + x2 = 1500 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 = 1500 + 100 Reorder the terms: 100 + 20x + x2 = 1500 + 100 Combine like terms: 1500 + 100 = 1600 100 + 20x + x2 = 1600 Factor a perfect square on the left side: (x + 10)(x + 10) = 1600 Calculate the square root of the right side: 40 Break this problem into two subproblems by setting (x + 10) equal to 40 and -40.Subproblem 1
x + 10 = 40 Simplifying x + 10 = 40 Reorder the terms: 10 + x = 40 Solving 10 + x = 40 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 = 40 + -10 Combine like terms: 10 + -10 = 0 0 + x = 40 + -10 x = 40 + -10 Combine like terms: 40 + -10 = 30 x = 30 Simplifying x = 30Subproblem 2
x + 10 = -40 Simplifying x + 10 = -40 Reorder the terms: 10 + x = -40 Solving 10 + x = -40 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 = -40 + -10 Combine like terms: 10 + -10 = 0 0 + x = -40 + -10 x = -40 + -10 Combine like terms: -40 + -10 = -50 x = -50 Simplifying x = -50Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, -50}
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