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Simplifying 4.5x2 + -4x2 + 4x + 3.5 = 0 Reorder the terms: 3.5 + 4x + 4.5x2 + -4x2 = 0 Combine like terms: 4.5x2 + -4x2 = 0.5x2 3.5 + 4x + 0.5x2 = 0 Solving 3.5 + 4x + 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'. 7 + 8x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 8x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 8x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8x + x2 = 0 + -7 8x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 8x + x2 = -7 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -7 + 16 Reorder the terms: 16 + 8x + x2 = -7 + 16 Combine like terms: -7 + 16 = 9 16 + 8x + x2 = 9 Factor a perfect square on the left side: (x + 4)(x + 4) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + 4) equal to 3 and -3.Subproblem 1
x + 4 = 3 Simplifying x + 4 = 3 Reorder the terms: 4 + x = 3 Solving 4 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3 + -4 x = 3 + -4 Combine like terms: 3 + -4 = -1 x = -1 Simplifying x = -1Subproblem 2
x + 4 = -3 Simplifying x + 4 = -3 Reorder the terms: 4 + x = -3 Solving 4 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3 + -4 x = -3 + -4 Combine like terms: -3 + -4 = -7 x = -7 Simplifying x = -7Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1, -7}
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