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Simplifying 0 = 5x2 + -40x + -12 Reorder the terms: 0 = -12 + -40x + 5x2 Solving 0 = -12 + -40x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 12 = 12 12 + 40x + -5x2 = -12 + -40x + 5x2 + 12 + 40x + -5x2 Reorder the terms: 12 + 40x + -5x2 = -12 + 12 + -40x + 40x + 5x2 + -5x2 Combine like terms: -12 + 12 = 0 12 + 40x + -5x2 = 0 + -40x + 40x + 5x2 + -5x2 12 + 40x + -5x2 = -40x + 40x + 5x2 + -5x2 Combine like terms: -40x + 40x = 0 12 + 40x + -5x2 = 0 + 5x2 + -5x2 12 + 40x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 12 + 40x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + -8x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -8x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -8x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -8x + x2 = 0 + 2.4 -8x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -8x + x2 = 2.4 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 2.4 + 16 Reorder the terms: 16 + -8x + x2 = 2.4 + 16 Combine like terms: 2.4 + 16 = 18.4 16 + -8x + x2 = 18.4 Factor a perfect square on the left side: (x + -4)(x + -4) = 18.4 Calculate the square root of the right side: 4.289522118 Break this problem into two subproblems by setting (x + -4) equal to 4.289522118 and -4.289522118.Subproblem 1
x + -4 = 4.289522118 Simplifying x + -4 = 4.289522118 Reorder the terms: -4 + x = 4.289522118 Solving -4 + x = 4.289522118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.289522118 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.289522118 + 4 x = 4.289522118 + 4 Combine like terms: 4.289522118 + 4 = 8.289522118 x = 8.289522118 Simplifying x = 8.289522118Subproblem 2
x + -4 = -4.289522118 Simplifying x + -4 = -4.289522118 Reorder the terms: -4 + x = -4.289522118 Solving -4 + x = -4.289522118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.289522118 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.289522118 + 4 x = -4.289522118 + 4 Combine like terms: -4.289522118 + 4 = -0.289522118 x = -0.289522118 Simplifying x = -0.289522118Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.289522118, -0.289522118}
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