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Simplifying 7x2 + -8x + -150 = 0 Reorder the terms: -150 + -8x + 7x2 = 0 Solving -150 + -8x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -21.42857143 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '21.42857143' to each side of the equation. -21.42857143 + -1.142857143x + 21.42857143 + x2 = 0 + 21.42857143 Reorder the terms: -21.42857143 + 21.42857143 + -1.142857143x + x2 = 0 + 21.42857143 Combine like terms: -21.42857143 + 21.42857143 = 0.00000000 0.00000000 + -1.142857143x + x2 = 0 + 21.42857143 -1.142857143x + x2 = 0 + 21.42857143 Combine like terms: 0 + 21.42857143 = 21.42857143 -1.142857143x + x2 = 21.42857143 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 21.42857143 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 21.42857143 + 0.3265306123 Combine like terms: 21.42857143 + 0.3265306123 = 21.7551020423 0.3265306123 + -1.142857143x + x2 = 21.7551020423 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 21.7551020423 Calculate the square root of the right side: 4.664236491 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 4.664236491 and -4.664236491.Subproblem 1
x + -0.5714285715 = 4.664236491 Simplifying x + -0.5714285715 = 4.664236491 Reorder the terms: -0.5714285715 + x = 4.664236491 Solving -0.5714285715 + x = 4.664236491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 4.664236491 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 4.664236491 + 0.5714285715 x = 4.664236491 + 0.5714285715 Combine like terms: 4.664236491 + 0.5714285715 = 5.2356650625 x = 5.2356650625 Simplifying x = 5.2356650625Subproblem 2
x + -0.5714285715 = -4.664236491 Simplifying x + -0.5714285715 = -4.664236491 Reorder the terms: -0.5714285715 + x = -4.664236491 Solving -0.5714285715 + x = -4.664236491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -4.664236491 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -4.664236491 + 0.5714285715 x = -4.664236491 + 0.5714285715 Combine like terms: -4.664236491 + 0.5714285715 = -4.0928079195 x = -4.0928079195 Simplifying x = -4.0928079195Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.2356650625, -4.0928079195}
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