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Simplifying 5x2 + -12x + -1.6 = 0 Reorder the terms: -1.6 + -12x + 5x2 = 0 Solving -1.6 + -12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.32 + -2.4x + x2 = 0 Move the constant term to the right: Add '0.32' to each side of the equation. -0.32 + -2.4x + 0.32 + x2 = 0 + 0.32 Reorder the terms: -0.32 + 0.32 + -2.4x + x2 = 0 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + -2.4x + x2 = 0 + 0.32 -2.4x + x2 = 0 + 0.32 Combine like terms: 0 + 0.32 = 0.32 -2.4x + x2 = 0.32 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 0.32 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 0.32 + 1.44 Combine like terms: 0.32 + 1.44 = 1.76 1.44 + -2.4x + x2 = 1.76 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + -1.2) equal to 1.326649916 and -1.326649916.Subproblem 1
x + -1.2 = 1.326649916 Simplifying x + -1.2 = 1.326649916 Reorder the terms: -1.2 + x = 1.326649916 Solving -1.2 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.326649916 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.326649916 + 1.2 x = 1.326649916 + 1.2 Combine like terms: 1.326649916 + 1.2 = 2.526649916 x = 2.526649916 Simplifying x = 2.526649916Subproblem 2
x + -1.2 = -1.326649916 Simplifying x + -1.2 = -1.326649916 Reorder the terms: -1.2 + x = -1.326649916 Solving -1.2 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.326649916 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.326649916 + 1.2 x = -1.326649916 + 1.2 Combine like terms: -1.326649916 + 1.2 = -0.126649916 x = -0.126649916 Simplifying x = -0.126649916Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.526649916, -0.126649916}
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