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Simplifying 0.5x2 + 2x + 3 = x + 7 Reorder the terms: 3 + 2x + 0.5x2 = x + 7 Reorder the terms: 3 + 2x + 0.5x2 = 7 + x Solving 3 + 2x + 0.5x2 = 7 + x Solving for variable 'x'. Reorder the terms: 3 + -7 + 2x + -1x + 0.5x2 = 7 + x + -7 + -1x Combine like terms: 3 + -7 = -4 -4 + 2x + -1x + 0.5x2 = 7 + x + -7 + -1x Combine like terms: 2x + -1x = 1x -4 + 1x + 0.5x2 = 7 + x + -7 + -1x Reorder the terms: -4 + 1x + 0.5x2 = 7 + -7 + x + -1x Combine like terms: 7 + -7 = 0 -4 + 1x + 0.5x2 = 0 + x + -1x -4 + 1x + 0.5x2 = x + -1x Combine like terms: x + -1x = 0 -4 + 1x + 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'. -8 + 2x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 2x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 2x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2x + x2 = 0 + 8 2x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 2x + x2 = 8 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 8 + 1 Reorder the terms: 1 + 2x + x2 = 8 + 1 Combine like terms: 8 + 1 = 9 1 + 2x + x2 = 9 Factor a perfect square on the left side: (x + 1)(x + 1) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + 1) equal to 3 and -3.Subproblem 1
x + 1 = 3 Simplifying x + 1 = 3 Reorder the terms: 1 + x = 3 Solving 1 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3 + -1 x = 3 + -1 Combine like terms: 3 + -1 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 1 = -3 Simplifying x + 1 = -3 Reorder the terms: 1 + x = -3 Solving 1 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3 + -1 x = -3 + -1 Combine like terms: -3 + -1 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -4}
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