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Simplifying 0 = 5x2 + 12x + -20 Reorder the terms: 0 = -20 + 12x + 5x2 Solving 0 = -20 + 12x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 20 = 20 20 + -12x + -5x2 = -20 + 12x + 5x2 + 20 + -12x + -5x2 Reorder the terms: 20 + -12x + -5x2 = -20 + 20 + 12x + -12x + 5x2 + -5x2 Combine like terms: -20 + 20 = 0 20 + -12x + -5x2 = 0 + 12x + -12x + 5x2 + -5x2 20 + -12x + -5x2 = 12x + -12x + 5x2 + -5x2 Combine like terms: 12x + -12x = 0 20 + -12x + -5x2 = 0 + 5x2 + -5x2 20 + -12x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 20 + -12x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4 + 2.4x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2.4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.4x + x2 = 0 + 4 2.4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.4x + x2 = 4 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 = 4 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 4 + 1.44 Combine like terms: 4 + 1.44 = 5.44 1.44 + 2.4x + x2 = 5.44 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 5.44 Calculate the square root of the right side: 2.332380758 Break this problem into two subproblems by setting (x + 1.2) equal to 2.332380758 and -2.332380758.Subproblem 1
x + 1.2 = 2.332380758 Simplifying x + 1.2 = 2.332380758 Reorder the terms: 1.2 + x = 2.332380758 Solving 1.2 + x = 2.332380758 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 = 2.332380758 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 2.332380758 + -1.2 x = 2.332380758 + -1.2 Combine like terms: 2.332380758 + -1.2 = 1.132380758 x = 1.132380758 Simplifying x = 1.132380758Subproblem 2
x + 1.2 = -2.332380758 Simplifying x + 1.2 = -2.332380758 Reorder the terms: 1.2 + x = -2.332380758 Solving 1.2 + x = -2.332380758 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 = -2.332380758 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -2.332380758 + -1.2 x = -2.332380758 + -1.2 Combine like terms: -2.332380758 + -1.2 = -3.532380758 x = -3.532380758 Simplifying x = -3.532380758Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.132380758, -3.532380758}
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