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Simplifying 5x = (4x + -3)(x + 7) Reorder the terms: 5x = (-3 + 4x)(x + 7) Reorder the terms: 5x = (-3 + 4x)(7 + x) Multiply (-3 + 4x) * (7 + x) 5x = (-3(7 + x) + 4x * (7 + x)) 5x = ((7 * -3 + x * -3) + 4x * (7 + x)) 5x = ((-21 + -3x) + 4x * (7 + x)) 5x = (-21 + -3x + (7 * 4x + x * 4x)) 5x = (-21 + -3x + (28x + 4x2)) Combine like terms: -3x + 28x = 25x 5x = (-21 + 25x + 4x2) Solving 5x = -21 + 25x + 4x2 Solving for variable 'x'. Reorder the terms: 21 + 5x + -25x + -4x2 = -21 + 25x + 4x2 + 21 + -25x + -4x2 Combine like terms: 5x + -25x = -20x 21 + -20x + -4x2 = -21 + 25x + 4x2 + 21 + -25x + -4x2 Reorder the terms: 21 + -20x + -4x2 = -21 + 21 + 25x + -25x + 4x2 + -4x2 Combine like terms: -21 + 21 = 0 21 + -20x + -4x2 = 0 + 25x + -25x + 4x2 + -4x2 21 + -20x + -4x2 = 25x + -25x + 4x2 + -4x2 Combine like terms: 25x + -25x = 0 21 + -20x + -4x2 = 0 + 4x2 + -4x2 21 + -20x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 21 + -20x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.25 + 5x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 5x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 5x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 5x + x2 = 0 + 5.25 5x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 5x + x2 = 5.25 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 5.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 5.25 + 6.25 Combine like terms: 5.25 + 6.25 = 11.5 6.25 + 5x + x2 = 11.5 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + 2.5) equal to 3.391164992 and -3.391164992.Subproblem 1
x + 2.5 = 3.391164992 Simplifying x + 2.5 = 3.391164992 Reorder the terms: 2.5 + x = 3.391164992 Solving 2.5 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.391164992 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.391164992 + -2.5 x = 3.391164992 + -2.5 Combine like terms: 3.391164992 + -2.5 = 0.891164992 x = 0.891164992 Simplifying x = 0.891164992Subproblem 2
x + 2.5 = -3.391164992 Simplifying x + 2.5 = -3.391164992 Reorder the terms: 2.5 + x = -3.391164992 Solving 2.5 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.391164992 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.391164992 + -2.5 x = -3.391164992 + -2.5 Combine like terms: -3.391164992 + -2.5 = -5.891164992 x = -5.891164992 Simplifying x = -5.891164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.891164992, -5.891164992}
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