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Simplifying 5x(x + -4) = 7x + 12 Reorder the terms: 5x(-4 + x) = 7x + 12 (-4 * 5x + x * 5x) = 7x + 12 (-20x + 5x2) = 7x + 12 Reorder the terms: -20x + 5x2 = 12 + 7x Solving -20x + 5x2 = 12 + 7x Solving for variable 'x'. Reorder the terms: -12 + -20x + -7x + 5x2 = 12 + 7x + -12 + -7x Combine like terms: -20x + -7x = -27x -12 + -27x + 5x2 = 12 + 7x + -12 + -7x Reorder the terms: -12 + -27x + 5x2 = 12 + -12 + 7x + -7x Combine like terms: 12 + -12 = 0 -12 + -27x + 5x2 = 0 + 7x + -7x -12 + -27x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -12 + -27x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -5.4x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -5.4x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -5.4x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -5.4x + x2 = 0 + 2.4 -5.4x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -5.4x + x2 = 2.4 The x term is -5.4x. Take half its coefficient (-2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. -5.4x + 7.29 + x2 = 2.4 + 7.29 Reorder the terms: 7.29 + -5.4x + x2 = 2.4 + 7.29 Combine like terms: 2.4 + 7.29 = 9.69 7.29 + -5.4x + x2 = 9.69 Factor a perfect square on the left side: (x + -2.7)(x + -2.7) = 9.69 Calculate the square root of the right side: 3.112876483 Break this problem into two subproblems by setting (x + -2.7) equal to 3.112876483 and -3.112876483.Subproblem 1
x + -2.7 = 3.112876483 Simplifying x + -2.7 = 3.112876483 Reorder the terms: -2.7 + x = 3.112876483 Solving -2.7 + x = 3.112876483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = 3.112876483 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = 3.112876483 + 2.7 x = 3.112876483 + 2.7 Combine like terms: 3.112876483 + 2.7 = 5.812876483 x = 5.812876483 Simplifying x = 5.812876483Subproblem 2
x + -2.7 = -3.112876483 Simplifying x + -2.7 = -3.112876483 Reorder the terms: -2.7 + x = -3.112876483 Solving -2.7 + x = -3.112876483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = -3.112876483 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = -3.112876483 + 2.7 x = -3.112876483 + 2.7 Combine like terms: -3.112876483 + 2.7 = -0.412876483 x = -0.412876483 Simplifying x = -0.412876483Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.812876483, -0.412876483}
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