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Simplifying 7x(10 + -1x) = 18 (10 * 7x + -1x * 7x) = 18 (70x + -7x2) = 18 Solving 70x + -7x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 70x + -7x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 70x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 2.571428571 + -10x + x2 = 0 Move the constant term to the right: Add '-2.571428571' to each side of the equation. 2.571428571 + -10x + -2.571428571 + x2 = 0 + -2.571428571 Reorder the terms: 2.571428571 + -2.571428571 + -10x + x2 = 0 + -2.571428571 Combine like terms: 2.571428571 + -2.571428571 = 0.000000000 0.000000000 + -10x + x2 = 0 + -2.571428571 -10x + x2 = 0 + -2.571428571 Combine like terms: 0 + -2.571428571 = -2.571428571 -10x + x2 = -2.571428571 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -2.571428571 + 25 Reorder the terms: 25 + -10x + x2 = -2.571428571 + 25 Combine like terms: -2.571428571 + 25 = 22.428571429 25 + -10x + x2 = 22.428571429 Factor a perfect square on the left side: (x + -5)(x + -5) = 22.428571429 Calculate the square root of the right side: 4.735881273 Break this problem into two subproblems by setting (x + -5) equal to 4.735881273 and -4.735881273.Subproblem 1
x + -5 = 4.735881273 Simplifying x + -5 = 4.735881273 Reorder the terms: -5 + x = 4.735881273 Solving -5 + x = 4.735881273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.735881273 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.735881273 + 5 x = 4.735881273 + 5 Combine like terms: 4.735881273 + 5 = 9.735881273 x = 9.735881273 Simplifying x = 9.735881273Subproblem 2
x + -5 = -4.735881273 Simplifying x + -5 = -4.735881273 Reorder the terms: -5 + x = -4.735881273 Solving -5 + x = -4.735881273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.735881273 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.735881273 + 5 x = -4.735881273 + 5 Combine like terms: -4.735881273 + 5 = 0.264118727 x = 0.264118727 Simplifying x = 0.264118727Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.735881273, 0.264118727}
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