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Simplifying 7x(x + -10) = 2x + -7 Reorder the terms: 7x(-10 + x) = 2x + -7 (-10 * 7x + x * 7x) = 2x + -7 (-70x + 7x2) = 2x + -7 Reorder the terms: -70x + 7x2 = -7 + 2x Solving -70x + 7x2 = -7 + 2x Solving for variable 'x'. Reorder the terms: 7 + -70x + -2x + 7x2 = -7 + 2x + 7 + -2x Combine like terms: -70x + -2x = -72x 7 + -72x + 7x2 = -7 + 2x + 7 + -2x Reorder the terms: 7 + -72x + 7x2 = -7 + 7 + 2x + -2x Combine like terms: -7 + 7 = 0 7 + -72x + 7x2 = 0 + 2x + -2x 7 + -72x + 7x2 = 2x + -2x Combine like terms: 2x + -2x = 0 7 + -72x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + -10.28571429x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -10.28571429x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -10.28571429x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10.28571429x + x2 = 0 + -1 -10.28571429x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -10.28571429x + x2 = -1 The x term is -10.28571429x. Take half its coefficient (-5.142857145). Square it (26.44897961) and add it to both sides. Add '26.44897961' to each side of the equation. -10.28571429x + 26.44897961 + x2 = -1 + 26.44897961 Reorder the terms: 26.44897961 + -10.28571429x + x2 = -1 + 26.44897961 Combine like terms: -1 + 26.44897961 = 25.44897961 26.44897961 + -10.28571429x + x2 = 25.44897961 Factor a perfect square on the left side: (x + -5.142857145)(x + -5.142857145) = 25.44897961 Calculate the square root of the right side: 5.044698168 Break this problem into two subproblems by setting (x + -5.142857145) equal to 5.044698168 and -5.044698168.Subproblem 1
x + -5.142857145 = 5.044698168 Simplifying x + -5.142857145 = 5.044698168 Reorder the terms: -5.142857145 + x = 5.044698168 Solving -5.142857145 + x = 5.044698168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.142857145' to each side of the equation. -5.142857145 + 5.142857145 + x = 5.044698168 + 5.142857145 Combine like terms: -5.142857145 + 5.142857145 = 0.000000000 0.000000000 + x = 5.044698168 + 5.142857145 x = 5.044698168 + 5.142857145 Combine like terms: 5.044698168 + 5.142857145 = 10.187555313 x = 10.187555313 Simplifying x = 10.187555313Subproblem 2
x + -5.142857145 = -5.044698168 Simplifying x + -5.142857145 = -5.044698168 Reorder the terms: -5.142857145 + x = -5.044698168 Solving -5.142857145 + x = -5.044698168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.142857145' to each side of the equation. -5.142857145 + 5.142857145 + x = -5.044698168 + 5.142857145 Combine like terms: -5.142857145 + 5.142857145 = 0.000000000 0.000000000 + x = -5.044698168 + 5.142857145 x = -5.044698168 + 5.142857145 Combine like terms: -5.044698168 + 5.142857145 = 0.098158977 x = 0.098158977 Simplifying x = 0.098158977Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.187555313, 0.098158977}
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