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Simplifying 5x(x + -4) = 12 Reorder the terms: 5x(-4 + x) = 12 (-4 * 5x + x * 5x) = 12 (-20x + 5x2) = 12 Solving -20x + 5x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -20x + 5x2 = 12 + -12 Combine like terms: 12 + -12 = 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 = 4.529822128 x = 4.529822128 Simplifying x = 4.529822128Subproblem 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 = -0.529822128 x = -0.529822128 Simplifying x = -0.529822128Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.529822128, -0.529822128}
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