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Simplifying 1.3 = 5 * 12x + -12x2 Multiply 5 * 12 1.3 = 60x + -12x2 Solving 1.3 = 60x + -12x2 Solving for variable 'x'. Reorder the terms: 1.3 + -60x + 12x2 = 60x + -60x + -12x2 + 12x2 Combine like terms: 60x + -60x = 0 1.3 + -60x + 12x2 = 0 + -12x2 + 12x2 1.3 + -60x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 1.3 + -60x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.1083333333 + -5x + x2 = 0 Move the constant term to the right: Add '-0.1083333333' to each side of the equation. 0.1083333333 + -5x + -0.1083333333 + x2 = 0 + -0.1083333333 Reorder the terms: 0.1083333333 + -0.1083333333 + -5x + x2 = 0 + -0.1083333333 Combine like terms: 0.1083333333 + -0.1083333333 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + -0.1083333333 -5x + x2 = 0 + -0.1083333333 Combine like terms: 0 + -0.1083333333 = -0.1083333333 -5x + x2 = -0.1083333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.1083333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.1083333333 + 6.25 Combine like terms: -0.1083333333 + 6.25 = 6.1416666667 6.25 + -5x + x2 = 6.1416666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.1416666667 Calculate the square root of the right side: 2.478238622 Break this problem into two subproblems by setting (x + -2.5) equal to 2.478238622 and -2.478238622.Subproblem 1
x + -2.5 = 2.478238622 Simplifying x + -2.5 = 2.478238622 Reorder the terms: -2.5 + x = 2.478238622 Solving -2.5 + x = 2.478238622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.478238622 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.478238622 + 2.5 x = 2.478238622 + 2.5 Combine like terms: 2.478238622 + 2.5 = 4.978238622 x = 4.978238622 Simplifying x = 4.978238622Subproblem 2
x + -2.5 = -2.478238622 Simplifying x + -2.5 = -2.478238622 Reorder the terms: -2.5 + x = -2.478238622 Solving -2.5 + x = -2.478238622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.478238622 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.478238622 + 2.5 x = -2.478238622 + 2.5 Combine like terms: -2.478238622 + 2.5 = 0.021761378 x = 0.021761378 Simplifying x = 0.021761378Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.978238622, 0.021761378}
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