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Simplifying 0.5x2 + 2x = 22.5 Reorder the terms: 2x + 0.5x2 = 22.5 Solving 2x + 0.5x2 = 22.5 Solving for variable 'x'. Reorder the terms: -22.5 + 2x + 0.5x2 = 22.5 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 -22.5 + 2x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -45 + 4x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 4x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 4x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 4x + x2 = 0 + 45 4x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 4x + x2 = 45 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 45 + 4 Reorder the terms: 4 + 4x + x2 = 45 + 4 Combine like terms: 45 + 4 = 49 4 + 4x + x2 = 49 Factor a perfect square on the left side: (x + 2)(x + 2) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (x + 2) equal to 7 and -7.Subproblem 1
x + 2 = 7 Simplifying x + 2 = 7 Reorder the terms: 2 + x = 7 Solving 2 + x = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 7 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7 + -2 x = 7 + -2 Combine like terms: 7 + -2 = 5 x = 5 Simplifying x = 5Subproblem 2
x + 2 = -7 Simplifying x + 2 = -7 Reorder the terms: 2 + x = -7 Solving 2 + x = -7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -7 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7 + -2 x = -7 + -2 Combine like terms: -7 + -2 = -9 x = -9 Simplifying x = -9Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -9}
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