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Simplifying 5x(x + -4) = 3x + 4 Reorder the terms: 5x(-4 + x) = 3x + 4 (-4 * 5x + x * 5x) = 3x + 4 (-20x + 5x2) = 3x + 4 Reorder the terms: -20x + 5x2 = 4 + 3x Solving -20x + 5x2 = 4 + 3x Solving for variable 'x'. Reorder the terms: -4 + -20x + -3x + 5x2 = 4 + 3x + -4 + -3x Combine like terms: -20x + -3x = -23x -4 + -23x + 5x2 = 4 + 3x + -4 + -3x Reorder the terms: -4 + -23x + 5x2 = 4 + -4 + 3x + -3x Combine like terms: 4 + -4 = 0 -4 + -23x + 5x2 = 0 + 3x + -3x -4 + -23x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -4 + -23x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -4.6x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -4.6x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -4.6x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -4.6x + x2 = 0 + 0.8 -4.6x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -4.6x + x2 = 0.8 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 0.8 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 0.8 + 5.29 Combine like terms: 0.8 + 5.29 = 6.09 5.29 + -4.6x + x2 = 6.09 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 6.09 Calculate the square root of the right side: 2.467792536 Break this problem into two subproblems by setting (x + -2.3) equal to 2.467792536 and -2.467792536.Subproblem 1
x + -2.3 = 2.467792536 Simplifying x + -2.3 = 2.467792536 Reorder the terms: -2.3 + x = 2.467792536 Solving -2.3 + x = 2.467792536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 2.467792536 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 2.467792536 + 2.3 x = 2.467792536 + 2.3 Combine like terms: 2.467792536 + 2.3 = 4.767792536 x = 4.767792536 Simplifying x = 4.767792536Subproblem 2
x + -2.3 = -2.467792536 Simplifying x + -2.3 = -2.467792536 Reorder the terms: -2.3 + x = -2.467792536 Solving -2.3 + x = -2.467792536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -2.467792536 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -2.467792536 + 2.3 x = -2.467792536 + 2.3 Combine like terms: -2.467792536 + 2.3 = -0.167792536 x = -0.167792536 Simplifying x = -0.167792536Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.767792536, -0.167792536}
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