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Simplifying 7x2 = 70x + -17 Reorder the terms: 7x2 = -17 + 70x Solving 7x2 = -17 + 70x Solving for variable 'x'. Reorder the terms: 17 + -70x + 7x2 = -17 + 70x + 17 + -70x Reorder the terms: 17 + -70x + 7x2 = -17 + 17 + 70x + -70x Combine like terms: -17 + 17 = 0 17 + -70x + 7x2 = 0 + 70x + -70x 17 + -70x + 7x2 = 70x + -70x Combine like terms: 70x + -70x = 0 17 + -70x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.428571429 + -10x + x2 = 0 Move the constant term to the right: Add '-2.428571429' to each side of the equation. 2.428571429 + -10x + -2.428571429 + x2 = 0 + -2.428571429 Reorder the terms: 2.428571429 + -2.428571429 + -10x + x2 = 0 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + -10x + x2 = 0 + -2.428571429 -10x + x2 = 0 + -2.428571429 Combine like terms: 0 + -2.428571429 = -2.428571429 -10x + x2 = -2.428571429 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 = -2.428571429 + 25 Reorder the terms: 25 + -10x + x2 = -2.428571429 + 25 Combine like terms: -2.428571429 + 25 = 22.571428571 25 + -10x + x2 = 22.571428571 Factor a perfect square on the left side: (x + -5)(x + -5) = 22.571428571 Calculate the square root of the right side: 4.750939757 Break this problem into two subproblems by setting (x + -5) equal to 4.750939757 and -4.750939757.Subproblem 1
x + -5 = 4.750939757 Simplifying x + -5 = 4.750939757 Reorder the terms: -5 + x = 4.750939757 Solving -5 + x = 4.750939757 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 = 4.750939757 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.750939757 + 5 x = 4.750939757 + 5 Combine like terms: 4.750939757 + 5 = 9.750939757 x = 9.750939757 Simplifying x = 9.750939757Subproblem 2
x + -5 = -4.750939757 Simplifying x + -5 = -4.750939757 Reorder the terms: -5 + x = -4.750939757 Solving -5 + x = -4.750939757 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 = -4.750939757 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.750939757 + 5 x = -4.750939757 + 5 Combine like terms: -4.750939757 + 5 = 0.249060243 x = 0.249060243 Simplifying x = 0.249060243Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.750939757, 0.249060243}
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