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Simplifying 4x(x + -5) + (7 + x) = 47 Reorder the terms: 4x(-5 + x) + (7 + x) = 47 (-5 * 4x + x * 4x) + (7 + x) = 47 (-20x + 4x2) + (7 + x) = 47 Remove parenthesis around (7 + x) -20x + 4x2 + 7 + x = 47 Reorder the terms: 7 + -20x + x + 4x2 = 47 Combine like terms: -20x + x = -19x 7 + -19x + 4x2 = 47 Solving 7 + -19x + 4x2 = 47 Solving for variable 'x'. Reorder the terms: 7 + -47 + -19x + 4x2 = 47 + -47 Combine like terms: 7 + -47 = -40 -40 + -19x + 4x2 = 47 + -47 Combine like terms: 47 + -47 = 0 -40 + -19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10 + -4.75x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -4.75x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -4.75x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4.75x + x2 = 0 + 10 -4.75x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4.75x + x2 = 10 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 10 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 10 + 5.640625 Combine like terms: 10 + 5.640625 = 15.640625 5.640625 + -4.75x + x2 = 15.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 15.640625 Calculate the square root of the right side: 3.954823005 Break this problem into two subproblems by setting (x + -2.375) equal to 3.954823005 and -3.954823005.Subproblem 1
x + -2.375 = 3.954823005 Simplifying x + -2.375 = 3.954823005 Reorder the terms: -2.375 + x = 3.954823005 Solving -2.375 + x = 3.954823005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 3.954823005 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 3.954823005 + 2.375 x = 3.954823005 + 2.375 Combine like terms: 3.954823005 + 2.375 = 6.329823005 x = 6.329823005 Simplifying x = 6.329823005Subproblem 2
x + -2.375 = -3.954823005 Simplifying x + -2.375 = -3.954823005 Reorder the terms: -2.375 + x = -3.954823005 Solving -2.375 + x = -3.954823005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -3.954823005 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -3.954823005 + 2.375 x = -3.954823005 + 2.375 Combine like terms: -3.954823005 + 2.375 = -1.579823005 x = -1.579823005 Simplifying x = -1.579823005Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.329823005, -1.579823005}
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