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Simplifying 2x + 7 + 5(x + 7) = 11x + 2x(3x + 7) Reorder the terms: 2x + 7 + 5(7 + x) = 11x + 2x(3x + 7) 2x + 7 + (7 * 5 + x * 5) = 11x + 2x(3x + 7) 2x + 7 + (35 + 5x) = 11x + 2x(3x + 7) Reorder the terms: 7 + 35 + 2x + 5x = 11x + 2x(3x + 7) Combine like terms: 7 + 35 = 42 42 + 2x + 5x = 11x + 2x(3x + 7) Combine like terms: 2x + 5x = 7x 42 + 7x = 11x + 2x(3x + 7) Reorder the terms: 42 + 7x = 11x + 2x(7 + 3x) 42 + 7x = 11x + (7 * 2x + 3x * 2x) 42 + 7x = 11x + (14x + 6x2) Combine like terms: 11x + 14x = 25x 42 + 7x = 25x + 6x2 Solving 42 + 7x = 25x + 6x2 Solving for variable 'x'. Combine like terms: 7x + -25x = -18x 42 + -18x + -6x2 = 25x + 6x2 + -25x + -6x2 Reorder the terms: 42 + -18x + -6x2 = 25x + -25x + 6x2 + -6x2 Combine like terms: 25x + -25x = 0 42 + -18x + -6x2 = 0 + 6x2 + -6x2 42 + -18x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 42 + -18x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(7 + -3x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 7 + -3x + -1x2 = 0 Solving 7 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + 3x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 3x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 3x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3x + x2 = 0 + 7 3x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 3x + x2 = 7 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 7 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 7 + 2.25 Combine like terms: 7 + 2.25 = 9.25 2.25 + 3x + x2 = 9.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + 1.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + 1.5 = 3.041381265 Simplifying x + 1.5 = 3.041381265 Reorder the terms: 1.5 + x = 3.041381265 Solving 1.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.041381265 + -1.5 x = 3.041381265 + -1.5 Combine like terms: 3.041381265 + -1.5 = 1.541381265 x = 1.541381265 Simplifying x = 1.541381265Subproblem 2
x + 1.5 = -3.041381265 Simplifying x + 1.5 = -3.041381265 Reorder the terms: 1.5 + x = -3.041381265 Solving 1.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.041381265 + -1.5 x = -3.041381265 + -1.5 Combine like terms: -3.041381265 + -1.5 = -4.541381265 x = -4.541381265 Simplifying x = -4.541381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.541381265, -4.541381265}Solution
x = {1.541381265, -4.541381265}
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