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Simplifying (24 + -0.5x2) + -14x = 0 Remove parenthesis around (24 + -0.5x2) 24 + -0.5x2 + -14x = 0 Reorder the terms: 24 + -14x + -0.5x2 = 0 Solving 24 + -14x + -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'. -48 + 28x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 28x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 28x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 28x + x2 = 0 + 48 28x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 28x + x2 = 48 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 48 + 196 Reorder the terms: 196 + 28x + x2 = 48 + 196 Combine like terms: 48 + 196 = 244 196 + 28x + x2 = 244 Factor a perfect square on the left side: (x + 14)(x + 14) = 244 Calculate the square root of the right side: 15.620499352 Break this problem into two subproblems by setting (x + 14) equal to 15.620499352 and -15.620499352.Subproblem 1
x + 14 = 15.620499352 Simplifying x + 14 = 15.620499352 Reorder the terms: 14 + x = 15.620499352 Solving 14 + x = 15.620499352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 15.620499352 + -14 Combine like terms: 14 + -14 = 0 0 + x = 15.620499352 + -14 x = 15.620499352 + -14 Combine like terms: 15.620499352 + -14 = 1.620499352 x = 1.620499352 Simplifying x = 1.620499352Subproblem 2
x + 14 = -15.620499352 Simplifying x + 14 = -15.620499352 Reorder the terms: 14 + x = -15.620499352 Solving 14 + x = -15.620499352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -15.620499352 + -14 Combine like terms: 14 + -14 = 0 0 + x = -15.620499352 + -14 x = -15.620499352 + -14 Combine like terms: -15.620499352 + -14 = -29.620499352 x = -29.620499352 Simplifying x = -29.620499352Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.620499352, -29.620499352}
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