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Simplifying 2x2 + -2x + 5.5 = 7 Reorder the terms: 5.5 + -2x + 2x2 = 7 Solving 5.5 + -2x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: 5.5 + -7 + -2x + 2x2 = 7 + -7 Combine like terms: 5.5 + -7 = -1.5 -1.5 + -2x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -1.5 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.75 + -1x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1x + x2 = 0 + 0.75 -1x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1x + x2 = 0.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.75 + 0.25 Combine like terms: 0.75 + 0.25 = 1 0.25 + -1x + x2 = 1 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + -0.5) equal to 1 and -1.Subproblem 1
x + -0.5 = 1 Simplifying x + -0.5 = 1 Reorder the terms: -0.5 + x = 1 Solving -0.5 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1 + 0.5 x = 1 + 0.5 Combine like terms: 1 + 0.5 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + -0.5 = -1 Simplifying x + -0.5 = -1 Reorder the terms: -0.5 + x = -1 Solving -0.5 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1 + 0.5 x = -1 + 0.5 Combine like terms: -1 + 0.5 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, -0.5}
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