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Simplifying 0.5x2 + -0.4x + -1.2 = 0 Reorder the terms: -1.2 + -0.4x + 0.5x2 = 0 Solving -1.2 + -0.4x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -2.4 + -0.8x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -0.8x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -0.8x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -0.8x + x2 = 0 + 2.4 -0.8x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -0.8x + x2 = 2.4 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 = 2.4 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 2.4 + 0.16 Combine like terms: 2.4 + 0.16 = 2.56 0.16 + -0.8x + x2 = 2.56 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 2.56 Calculate the square root of the right side: 1.6 Break this problem into two subproblems by setting (x + -0.4) equal to 1.6 and -1.6.Subproblem 1
x + -0.4 = 1.6 Simplifying x + -0.4 = 1.6 Reorder the terms: -0.4 + x = 1.6 Solving -0.4 + x = 1.6 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 = 1.6 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.6 + 0.4 x = 1.6 + 0.4 Combine like terms: 1.6 + 0.4 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -0.4 = -1.6 Simplifying x + -0.4 = -1.6 Reorder the terms: -0.4 + x = -1.6 Solving -0.4 + x = -1.6 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 = -1.6 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.6 + 0.4 x = -1.6 + 0.4 Combine like terms: -1.6 + 0.4 = -1.2 x = -1.2 Simplifying x = -1.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -1.2}
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