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Simplifying 8 + x(19 + -2x) = 6(11 + -1x) 8 + (19 * x + -2x * x) = 6(11 + -1x) 8 + (19x + -2x2) = 6(11 + -1x) 8 + 19x + -2x2 = (11 * 6 + -1x * 6) 8 + 19x + -2x2 = (66 + -6x) Solving 8 + 19x + -2x2 = 66 + -6x Solving for variable 'x'. Reorder the terms: 8 + -66 + 19x + 6x + -2x2 = 66 + -6x + -66 + 6x Combine like terms: 8 + -66 = -58 -58 + 19x + 6x + -2x2 = 66 + -6x + -66 + 6x Combine like terms: 19x + 6x = 25x -58 + 25x + -2x2 = 66 + -6x + -66 + 6x Reorder the terms: -58 + 25x + -2x2 = 66 + -66 + -6x + 6x Combine like terms: 66 + -66 = 0 -58 + 25x + -2x2 = 0 + -6x + 6x -58 + 25x + -2x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -58 + 25x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 29 + -12.5x + x2 = 0 Move the constant term to the right: Add '-29' to each side of the equation. 29 + -12.5x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + -12.5x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -12.5x + x2 = 0 + -29 -12.5x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 -12.5x + x2 = -29 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -29 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -29 + 39.0625 Combine like terms: -29 + 39.0625 = 10.0625 39.0625 + -12.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + -6.25) equal to 3.172144385 and -3.172144385.Subproblem 1
x + -6.25 = 3.172144385 Simplifying x + -6.25 = 3.172144385 Reorder the terms: -6.25 + x = 3.172144385 Solving -6.25 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 3.172144385 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 3.172144385 + 6.25 x = 3.172144385 + 6.25 Combine like terms: 3.172144385 + 6.25 = 9.422144385 x = 9.422144385 Simplifying x = 9.422144385Subproblem 2
x + -6.25 = -3.172144385 Simplifying x + -6.25 = -3.172144385 Reorder the terms: -6.25 + x = -3.172144385 Solving -6.25 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -3.172144385 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -3.172144385 + 6.25 x = -3.172144385 + 6.25 Combine like terms: -3.172144385 + 6.25 = 3.077855615 x = 3.077855615 Simplifying x = 3.077855615Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.422144385, 3.077855615}
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