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Simplifying 2x2 + 8x = 4.5 Reorder the terms: 8x + 2x2 = 4.5 Solving 8x + 2x2 = 4.5 Solving for variable 'x'. Reorder the terms: -4.5 + 8x + 2x2 = 4.5 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 -4.5 + 8x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.25 + 4x + x2 = 0.0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 4x + 2.25 + x2 = 0.0 + 2.25 Reorder the terms: -2.25 + 2.25 + 4x + x2 = 0.0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 4x + x2 = 0.0 + 2.25 4x + x2 = 0.0 + 2.25 Combine like terms: 0.0 + 2.25 = 2.25 4x + x2 = 2.25 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 = 2.25 + 4 Reorder the terms: 4 + 4x + x2 = 2.25 + 4 Combine like terms: 2.25 + 4 = 6.25 4 + 4x + x2 = 6.25 Factor a perfect square on the left side: (x + 2)(x + 2) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + 2) equal to 2.5 and -2.5.Subproblem 1
x + 2 = 2.5 Simplifying x + 2 = 2.5 Reorder the terms: 2 + x = 2.5 Solving 2 + x = 2.5 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 = 2.5 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.5 + -2 x = 2.5 + -2 Combine like terms: 2.5 + -2 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 2 = -2.5 Simplifying x + 2 = -2.5 Reorder the terms: 2 + x = -2.5 Solving 2 + x = -2.5 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 = -2.5 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.5 + -2 x = -2.5 + -2 Combine like terms: -2.5 + -2 = -4.5 x = -4.5 Simplifying x = -4.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -4.5}
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