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Simplifying 9x + -4 = 4(x + -1) * 5x + 4 Reorder the terms: -4 + 9x = 4(x + -1) * 5x + 4 Reorder the terms: -4 + 9x = 4(-1 + x) * 5x + 4 Reorder the terms for easier multiplication: -4 + 9x = 4 * 5x(-1 + x) + 4 Multiply 4 * 5 -4 + 9x = 20x(-1 + x) + 4 -4 + 9x = (-1 * 20x + x * 20x) + 4 -4 + 9x = (-20x + 20x2) + 4 Reorder the terms: -4 + 9x = 4 + -20x + 20x2 Solving -4 + 9x = 4 + -20x + 20x2 Solving for variable 'x'. Reorder the terms: -4 + -4 + 9x + 20x + -20x2 = 4 + -20x + 20x2 + -4 + 20x + -20x2 Combine like terms: -4 + -4 = -8 -8 + 9x + 20x + -20x2 = 4 + -20x + 20x2 + -4 + 20x + -20x2 Combine like terms: 9x + 20x = 29x -8 + 29x + -20x2 = 4 + -20x + 20x2 + -4 + 20x + -20x2 Reorder the terms: -8 + 29x + -20x2 = 4 + -4 + -20x + 20x + 20x2 + -20x2 Combine like terms: 4 + -4 = 0 -8 + 29x + -20x2 = 0 + -20x + 20x + 20x2 + -20x2 -8 + 29x + -20x2 = -20x + 20x + 20x2 + -20x2 Combine like terms: -20x + 20x = 0 -8 + 29x + -20x2 = 0 + 20x2 + -20x2 -8 + 29x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -8 + 29x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. 0.4 + -1.45x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.45x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.45x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.45x + x2 = 0 + -0.4 -1.45x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.45x + x2 = -0.4 The x term is -1.45x. Take half its coefficient (-0.725). Square it (0.525625) and add it to both sides. Add '0.525625' to each side of the equation. -1.45x + 0.525625 + x2 = -0.4 + 0.525625 Reorder the terms: 0.525625 + -1.45x + x2 = -0.4 + 0.525625 Combine like terms: -0.4 + 0.525625 = 0.125625 0.525625 + -1.45x + x2 = 0.125625 Factor a perfect square on the left side: (x + -0.725)(x + -0.725) = 0.125625 Calculate the square root of the right side: 0.354436172 Break this problem into two subproblems by setting (x + -0.725) equal to 0.354436172 and -0.354436172.Subproblem 1
x + -0.725 = 0.354436172 Simplifying x + -0.725 = 0.354436172 Reorder the terms: -0.725 + x = 0.354436172 Solving -0.725 + x = 0.354436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.725' to each side of the equation. -0.725 + 0.725 + x = 0.354436172 + 0.725 Combine like terms: -0.725 + 0.725 = 0.000 0.000 + x = 0.354436172 + 0.725 x = 0.354436172 + 0.725 Combine like terms: 0.354436172 + 0.725 = 1.079436172 x = 1.079436172 Simplifying x = 1.079436172Subproblem 2
x + -0.725 = -0.354436172 Simplifying x + -0.725 = -0.354436172 Reorder the terms: -0.725 + x = -0.354436172 Solving -0.725 + x = -0.354436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.725' to each side of the equation. -0.725 + 0.725 + x = -0.354436172 + 0.725 Combine like terms: -0.725 + 0.725 = 0.000 0.000 + x = -0.354436172 + 0.725 x = -0.354436172 + 0.725 Combine like terms: -0.354436172 + 0.725 = 0.370563828 x = 0.370563828 Simplifying x = 0.370563828Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.079436172, 0.370563828}
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