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Simplifying 4x(x + -5) = 3x + 5(x + -5) Reorder the terms: 4x(-5 + x) = 3x + 5(x + -5) (-5 * 4x + x * 4x) = 3x + 5(x + -5) (-20x + 4x2) = 3x + 5(x + -5) Reorder the terms: -20x + 4x2 = 3x + 5(-5 + x) -20x + 4x2 = 3x + (-5 * 5 + x * 5) -20x + 4x2 = 3x + (-25 + 5x) Reorder the terms: -20x + 4x2 = -25 + 3x + 5x Combine like terms: 3x + 5x = 8x -20x + 4x2 = -25 + 8x Solving -20x + 4x2 = -25 + 8x Solving for variable 'x'. Reorder the terms: 25 + -20x + -8x + 4x2 = -25 + 8x + 25 + -8x Combine like terms: -20x + -8x = -28x 25 + -28x + 4x2 = -25 + 8x + 25 + -8x Reorder the terms: 25 + -28x + 4x2 = -25 + 25 + 8x + -8x Combine like terms: -25 + 25 = 0 25 + -28x + 4x2 = 0 + 8x + -8x 25 + -28x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 25 + -28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + -7x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -7x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -7x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -7x + x2 = 0 + -6.25 -7x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -7x + x2 = -6.25 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -6.25 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -6.25 + 12.25 Combine like terms: -6.25 + 12.25 = 6 12.25 + -7x + x2 = 6 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -3.5) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -3.5 = 2.449489743 Simplifying x + -3.5 = 2.449489743 Reorder the terms: -3.5 + x = 2.449489743 Solving -3.5 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.449489743 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.449489743 + 3.5 x = 2.449489743 + 3.5 Combine like terms: 2.449489743 + 3.5 = 5.949489743 x = 5.949489743 Simplifying x = 5.949489743Subproblem 2
x + -3.5 = -2.449489743 Simplifying x + -3.5 = -2.449489743 Reorder the terms: -3.5 + x = -2.449489743 Solving -3.5 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.449489743 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.449489743 + 3.5 x = -2.449489743 + 3.5 Combine like terms: -2.449489743 + 3.5 = 1.050510257 x = 1.050510257 Simplifying x = 1.050510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.949489743, 1.050510257}
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