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Simplifying 0.5x2 = -0.4x + 2.7 Reorder the terms: 0.5x2 = 2.7 + -0.4x Solving 0.5x2 = 2.7 + -0.4x Solving for variable 'x'. Reorder the terms: -2.7 + 0.4x + 0.5x2 = 2.7 + -0.4x + -2.7 + 0.4x Reorder the terms: -2.7 + 0.4x + 0.5x2 = 2.7 + -2.7 + -0.4x + 0.4x Combine like terms: 2.7 + -2.7 = 0.0 -2.7 + 0.4x + 0.5x2 = 0.0 + -0.4x + 0.4x -2.7 + 0.4x + 0.5x2 = -0.4x + 0.4x Combine like terms: -0.4x + 0.4x = 0.0 -2.7 + 0.4x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -5.4 + 0.8x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 0.8x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 0.8x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 0.8x + x2 = 0 + 5.4 0.8x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 0.8x + x2 = 5.4 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 5.4 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 5.4 + 0.16 Combine like terms: 5.4 + 0.16 = 5.56 0.16 + 0.8x + x2 = 5.56 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 5.56 Calculate the square root of the right side: 2.357965225 Break this problem into two subproblems by setting (x + 0.4) equal to 2.357965225 and -2.357965225.Subproblem 1
x + 0.4 = 2.357965225 Simplifying x + 0.4 = 2.357965225 Reorder the terms: 0.4 + x = 2.357965225 Solving 0.4 + x = 2.357965225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.357965225 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.357965225 + -0.4 x = 2.357965225 + -0.4 Combine like terms: 2.357965225 + -0.4 = 1.957965225 x = 1.957965225 Simplifying x = 1.957965225Subproblem 2
x + 0.4 = -2.357965225 Simplifying x + 0.4 = -2.357965225 Reorder the terms: 0.4 + x = -2.357965225 Solving 0.4 + x = -2.357965225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.357965225 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.357965225 + -0.4 x = -2.357965225 + -0.4 Combine like terms: -2.357965225 + -0.4 = -2.757965225 x = -2.757965225 Simplifying x = -2.757965225Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.957965225, -2.757965225}
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