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Simplifying 0 = -7x2 + 8x + 10 Reorder the terms: 0 = 10 + 8x + -7x2 Solving 0 = 10 + 8x + -7x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -8x + 7x2 = 10 + 8x + -7x2 + -10 + -8x + 7x2 Reorder the terms: -10 + -8x + 7x2 = 10 + -10 + 8x + -8x + -7x2 + 7x2 Combine like terms: 10 + -10 = 0 -10 + -8x + 7x2 = 0 + 8x + -8x + -7x2 + 7x2 -10 + -8x + 7x2 = 8x + -8x + -7x2 + 7x2 Combine like terms: 8x + -8x = 0 -10 + -8x + 7x2 = 0 + -7x2 + 7x2 -10 + -8x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -10 + -8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -1.142857143x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -1.142857143x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -1.142857143x + x2 = 0 + 1.428571429 -1.142857143x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -1.142857143x + x2 = 1.428571429 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 = 1.428571429 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 1.428571429 + 0.3265306123 Combine like terms: 1.428571429 + 0.3265306123 = 1.7551020413 0.3265306123 + -1.142857143x + x2 = 1.7551020413 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 1.7551020413 Calculate the square root of the right side: 1.324802642 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.324802642 and -1.324802642.Subproblem 1
x + -0.5714285715 = 1.324802642 Simplifying x + -0.5714285715 = 1.324802642 Reorder the terms: -0.5714285715 + x = 1.324802642 Solving -0.5714285715 + x = 1.324802642 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 = 1.324802642 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.324802642 + 0.5714285715 x = 1.324802642 + 0.5714285715 Combine like terms: 1.324802642 + 0.5714285715 = 1.8962312135 x = 1.8962312135 Simplifying x = 1.8962312135Subproblem 2
x + -0.5714285715 = -1.324802642 Simplifying x + -0.5714285715 = -1.324802642 Reorder the terms: -0.5714285715 + x = -1.324802642 Solving -0.5714285715 + x = -1.324802642 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 = -1.324802642 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.324802642 + 0.5714285715 x = -1.324802642 + 0.5714285715 Combine like terms: -1.324802642 + 0.5714285715 = -0.7533740705 x = -0.7533740705 Simplifying x = -0.7533740705Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8962312135, -0.7533740705}
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