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Simplifying 4x(x + -1) = 5x + -4 Reorder the terms: 4x(-1 + x) = 5x + -4 (-1 * 4x + x * 4x) = 5x + -4 (-4x + 4x2) = 5x + -4 Reorder the terms: -4x + 4x2 = -4 + 5x Solving -4x + 4x2 = -4 + 5x Solving for variable 'x'. Reorder the terms: 4 + -4x + -5x + 4x2 = -4 + 5x + 4 + -5x Combine like terms: -4x + -5x = -9x 4 + -9x + 4x2 = -4 + 5x + 4 + -5x Reorder the terms: 4 + -9x + 4x2 = -4 + 4 + 5x + -5x Combine like terms: -4 + 4 = 0 4 + -9x + 4x2 = 0 + 5x + -5x 4 + -9x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 4 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + -2.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.25x + x2 = 0 + -1 -2.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.25x + x2 = -1 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -1 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -1 + 1.265625 Combine like terms: -1 + 1.265625 = 0.265625 1.265625 + -2.25x + x2 = 0.265625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (x + -1.125) equal to 0.515388203 and -0.515388203.Subproblem 1
x + -1.125 = 0.515388203 Simplifying x + -1.125 = 0.515388203 Reorder the terms: -1.125 + x = 0.515388203 Solving -1.125 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 0.515388203 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 0.515388203 + 1.125 x = 0.515388203 + 1.125 Combine like terms: 0.515388203 + 1.125 = 1.640388203 x = 1.640388203 Simplifying x = 1.640388203Subproblem 2
x + -1.125 = -0.515388203 Simplifying x + -1.125 = -0.515388203 Reorder the terms: -1.125 + x = -0.515388203 Solving -1.125 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -0.515388203 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -0.515388203 + 1.125 x = -0.515388203 + 1.125 Combine like terms: -0.515388203 + 1.125 = 0.609611797 x = 0.609611797 Simplifying x = 0.609611797Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.640388203, 0.609611797}
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