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Simplifying 0 = 5x2 + 20x + -12 Reorder the terms: 0 = -12 + 20x + 5x2 Solving 0 = -12 + 20x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 12 = 12 12 + -20x + -5x2 = -12 + 20x + 5x2 + 12 + -20x + -5x2 Reorder the terms: 12 + -20x + -5x2 = -12 + 12 + 20x + -20x + 5x2 + -5x2 Combine like terms: -12 + 12 = 0 12 + -20x + -5x2 = 0 + 20x + -20x + 5x2 + -5x2 12 + -20x + -5x2 = 20x + -20x + 5x2 + -5x2 Combine like terms: 20x + -20x = 0 12 + -20x + -5x2 = 0 + 5x2 + -5x2 12 + -20x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 12 + -20x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + 4x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 4x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 4x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 4x + x2 = 0 + 2.4 4x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 4x + x2 = 2.4 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 2.4 + 4 Reorder the terms: 4 + 4x + x2 = 2.4 + 4 Combine like terms: 2.4 + 4 = 6.4 4 + 4x + x2 = 6.4 Factor a perfect square on the left side: (x + 2)(x + 2) = 6.4 Calculate the square root of the right side: 2.529822128 Break this problem into two subproblems by setting (x + 2) equal to 2.529822128 and -2.529822128.Subproblem 1
x + 2 = 2.529822128 Simplifying x + 2 = 2.529822128 Reorder the terms: 2 + x = 2.529822128 Solving 2 + x = 2.529822128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.529822128 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.529822128 + -2 x = 2.529822128 + -2 Combine like terms: 2.529822128 + -2 = 0.529822128 x = 0.529822128 Simplifying x = 0.529822128Subproblem 2
x + 2 = -2.529822128 Simplifying x + 2 = -2.529822128 Reorder the terms: 2 + x = -2.529822128 Solving 2 + x = -2.529822128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.529822128 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.529822128 + -2 x = -2.529822128 + -2 Combine like terms: -2.529822128 + -2 = -4.529822128 x = -4.529822128 Simplifying x = -4.529822128Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.529822128, -4.529822128}
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