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Simplifying 12 + 10x + 0.5x2 = 40 Solving 12 + 10x + 0.5x2 = 40 Solving for variable 'x'. Reorder the terms: 12 + -40 + 10x + 0.5x2 = 40 + -40 Combine like terms: 12 + -40 = -28 -28 + 10x + 0.5x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -28 + 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'. -56 + 20x + x2 = 0 Move the constant term to the right: Add '56' to each side of the equation. -56 + 20x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 20x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 20x + x2 = 0 + 56 20x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 20x + x2 = 56 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 = 56 + 100 Reorder the terms: 100 + 20x + x2 = 56 + 100 Combine like terms: 56 + 100 = 156 100 + 20x + x2 = 156 Factor a perfect square on the left side: (x + 10)(x + 10) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + 10) equal to 12.489995997 and -12.489995997.Subproblem 1
x + 10 = 12.489995997 Simplifying x + 10 = 12.489995997 Reorder the terms: 10 + x = 12.489995997 Solving 10 + x = 12.489995997 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 = 12.489995997 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.489995997 + -10 x = 12.489995997 + -10 Combine like terms: 12.489995997 + -10 = 2.489995997 x = 2.489995997 Simplifying x = 2.489995997Subproblem 2
x + 10 = -12.489995997 Simplifying x + 10 = -12.489995997 Reorder the terms: 10 + x = -12.489995997 Solving 10 + x = -12.489995997 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 = -12.489995997 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.489995997 + -10 x = -12.489995997 + -10 Combine like terms: -12.489995997 + -10 = -22.489995997 x = -22.489995997 Simplifying x = -22.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.489995997, -22.489995997}
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