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Simplifying 2.5 = 2x2 + -4x Reorder the terms: 2.5 = -4x + 2x2 Solving 2.5 = -4x + 2x2 Solving for variable 'x'. Reorder the terms: 2.5 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 2.5 + 4x + -2x2 = 0 + 2x2 + -2x2 2.5 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 2.5 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.25 + -2x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2x + x2 = 0 + 1.25 -2x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2x + x2 = 1.25 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 = 1.25 + 1 Reorder the terms: 1 + -2x + x2 = 1.25 + 1 Combine like terms: 1.25 + 1 = 2.25 1 + -2x + x2 = 2.25 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + -1) equal to 1.5 and -1.5.Subproblem 1
x + -1 = 1.5 Simplifying x + -1 = 1.5 Reorder the terms: -1 + x = 1.5 Solving -1 + x = 1.5 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 = 1.5 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.5 + 1 x = 1.5 + 1 Combine like terms: 1.5 + 1 = 2.5 x = 2.5 Simplifying x = 2.5Subproblem 2
x + -1 = -1.5 Simplifying x + -1 = -1.5 Reorder the terms: -1 + x = -1.5 Solving -1 + x = -1.5 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 = -1.5 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.5 + 1 x = -1.5 + 1 Combine like terms: -1.5 + 1 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5, -0.5}
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