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Simplifying -12x(x + 6.2) = 60 Reorder the terms: -12x(6.2 + x) = 60 (6.2 * -12x + x * -12x) = 60 (-74.4x + -12x2) = 60 Solving -74.4x + -12x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + -74.4x + -12x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -74.4x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 5 + 6.2x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 6.2x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 6.2x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6.2x + x2 = 0 + -5 6.2x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 6.2x + x2 = -5 The x term is 6.2x. Take half its coefficient (3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. 6.2x + 9.61 + x2 = -5 + 9.61 Reorder the terms: 9.61 + 6.2x + x2 = -5 + 9.61 Combine like terms: -5 + 9.61 = 4.61 9.61 + 6.2x + x2 = 4.61 Factor a perfect square on the left side: (x + 3.1)(x + 3.1) = 4.61 Calculate the square root of the right side: 2.147091055 Break this problem into two subproblems by setting (x + 3.1) equal to 2.147091055 and -2.147091055.Subproblem 1
x + 3.1 = 2.147091055 Simplifying x + 3.1 = 2.147091055 Reorder the terms: 3.1 + x = 2.147091055 Solving 3.1 + x = 2.147091055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + x = 2.147091055 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = 2.147091055 + -3.1 x = 2.147091055 + -3.1 Combine like terms: 2.147091055 + -3.1 = -0.952908945 x = -0.952908945 Simplifying x = -0.952908945Subproblem 2
x + 3.1 = -2.147091055 Simplifying x + 3.1 = -2.147091055 Reorder the terms: 3.1 + x = -2.147091055 Solving 3.1 + x = -2.147091055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + x = -2.147091055 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = -2.147091055 + -3.1 x = -2.147091055 + -3.1 Combine like terms: -2.147091055 + -3.1 = -5.247091055 x = -5.247091055 Simplifying x = -5.247091055Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.952908945, -5.247091055}
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