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Simplifying 2x2 + x + -5.4 = 0 Reorder the terms: -5.4 + x + 2x2 = 0 Solving -5.4 + x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.7 + 0.5x + x2 = 0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + 0.5x + 2.7 + x2 = 0 + 2.7 Reorder the terms: -2.7 + 2.7 + 0.5x + x2 = 0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + 0.5x + x2 = 0 + 2.7 0.5x + x2 = 0 + 2.7 Combine like terms: 0 + 2.7 = 2.7 0.5x + x2 = 2.7 The x term is x. 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. 0.5x + 0.25 + x2 = 2.7 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 2.7 + 0.25 Combine like terms: 2.7 + 0.25 = 2.95 0.25 + 0.5x + x2 = 2.95 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.95 Calculate the square root of the right side: 1.717556404 Break this problem into two subproblems by setting (x + 0.5) equal to 1.717556404 and -1.717556404.Subproblem 1
x + 0.5 = 1.717556404 Simplifying x + 0.5 = 1.717556404 Reorder the terms: 0.5 + x = 1.717556404 Solving 0.5 + x = 1.717556404 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 = 1.717556404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.717556404 + -0.5 x = 1.717556404 + -0.5 Combine like terms: 1.717556404 + -0.5 = 1.217556404 x = 1.217556404 Simplifying x = 1.217556404Subproblem 2
x + 0.5 = -1.717556404 Simplifying x + 0.5 = -1.717556404 Reorder the terms: 0.5 + x = -1.717556404 Solving 0.5 + x = -1.717556404 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 = -1.717556404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.717556404 + -0.5 x = -1.717556404 + -0.5 Combine like terms: -1.717556404 + -0.5 = -2.217556404 x = -2.217556404 Simplifying x = -2.217556404Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.217556404, -2.217556404}
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