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Simplifying (4x + -20)(x + 7) + 4x + -20 = 23 + 5x Reorder the terms: (-20 + 4x)(x + 7) + 4x + -20 = 23 + 5x Reorder the terms: (-20 + 4x)(7 + x) + 4x + -20 = 23 + 5x Multiply (-20 + 4x) * (7 + x) (-20(7 + x) + 4x * (7 + x)) + 4x + -20 = 23 + 5x ((7 * -20 + x * -20) + 4x * (7 + x)) + 4x + -20 = 23 + 5x ((-140 + -20x) + 4x * (7 + x)) + 4x + -20 = 23 + 5x (-140 + -20x + (7 * 4x + x * 4x)) + 4x + -20 = 23 + 5x (-140 + -20x + (28x + 4x2)) + 4x + -20 = 23 + 5x Combine like terms: -20x + 28x = 8x (-140 + 8x + 4x2) + 4x + -20 = 23 + 5x Reorder the terms: -140 + -20 + 8x + 4x + 4x2 = 23 + 5x Combine like terms: -140 + -20 = -160 -160 + 8x + 4x + 4x2 = 23 + 5x Combine like terms: 8x + 4x = 12x -160 + 12x + 4x2 = 23 + 5x Solving -160 + 12x + 4x2 = 23 + 5x Solving for variable 'x'. Reorder the terms: -160 + -23 + 12x + -5x + 4x2 = 23 + 5x + -23 + -5x Combine like terms: -160 + -23 = -183 -183 + 12x + -5x + 4x2 = 23 + 5x + -23 + -5x Combine like terms: 12x + -5x = 7x -183 + 7x + 4x2 = 23 + 5x + -23 + -5x Reorder the terms: -183 + 7x + 4x2 = 23 + -23 + 5x + -5x Combine like terms: 23 + -23 = 0 -183 + 7x + 4x2 = 0 + 5x + -5x -183 + 7x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -183 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -45.75 + 1.75x + x2 = 0 Move the constant term to the right: Add '45.75' to each side of the equation. -45.75 + 1.75x + 45.75 + x2 = 0 + 45.75 Reorder the terms: -45.75 + 45.75 + 1.75x + x2 = 0 + 45.75 Combine like terms: -45.75 + 45.75 = 0.00 0.00 + 1.75x + x2 = 0 + 45.75 1.75x + x2 = 0 + 45.75 Combine like terms: 0 + 45.75 = 45.75 1.75x + x2 = 45.75 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 45.75 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 45.75 + 0.765625 Combine like terms: 45.75 + 0.765625 = 46.515625 0.765625 + 1.75x + x2 = 46.515625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 46.515625 Calculate the square root of the right side: 6.820236433 Break this problem into two subproblems by setting (x + 0.875) equal to 6.820236433 and -6.820236433.Subproblem 1
x + 0.875 = 6.820236433 Simplifying x + 0.875 = 6.820236433 Reorder the terms: 0.875 + x = 6.820236433 Solving 0.875 + x = 6.820236433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 6.820236433 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 6.820236433 + -0.875 x = 6.820236433 + -0.875 Combine like terms: 6.820236433 + -0.875 = 5.945236433 x = 5.945236433 Simplifying x = 5.945236433Subproblem 2
x + 0.875 = -6.820236433 Simplifying x + 0.875 = -6.820236433 Reorder the terms: 0.875 + x = -6.820236433 Solving 0.875 + x = -6.820236433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -6.820236433 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -6.820236433 + -0.875 x = -6.820236433 + -0.875 Combine like terms: -6.820236433 + -0.875 = -7.695236433 x = -7.695236433 Simplifying x = -7.695236433Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.945236433, -7.695236433}
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