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Simplifying 7x2 + 45x + 10 = 0 Reorder the terms: 10 + 45x + 7x2 = 0 Solving 10 + 45x + 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'. 1.428571429 + 6.428571429x + x2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + 6.428571429x + -1.428571429 + x2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + 6.428571429x + x2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + 6.428571429x + x2 = 0 + -1.428571429 6.428571429x + x2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 6.428571429x + x2 = -1.428571429 The x term is 6.428571429x. Take half its coefficient (3.214285715). Square it (10.33163266) and add it to both sides. Add '10.33163266' to each side of the equation. 6.428571429x + 10.33163266 + x2 = -1.428571429 + 10.33163266 Reorder the terms: 10.33163266 + 6.428571429x + x2 = -1.428571429 + 10.33163266 Combine like terms: -1.428571429 + 10.33163266 = 8.903061231 10.33163266 + 6.428571429x + x2 = 8.903061231 Factor a perfect square on the left side: (x + 3.214285715)(x + 3.214285715) = 8.903061231 Calculate the square root of the right side: 2.983799797 Break this problem into two subproblems by setting (x + 3.214285715) equal to 2.983799797 and -2.983799797.Subproblem 1
x + 3.214285715 = 2.983799797 Simplifying x + 3.214285715 = 2.983799797 Reorder the terms: 3.214285715 + x = 2.983799797 Solving 3.214285715 + x = 2.983799797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.214285715' to each side of the equation. 3.214285715 + -3.214285715 + x = 2.983799797 + -3.214285715 Combine like terms: 3.214285715 + -3.214285715 = 0.000000000 0.000000000 + x = 2.983799797 + -3.214285715 x = 2.983799797 + -3.214285715 Combine like terms: 2.983799797 + -3.214285715 = -0.230485918 x = -0.230485918 Simplifying x = -0.230485918Subproblem 2
x + 3.214285715 = -2.983799797 Simplifying x + 3.214285715 = -2.983799797 Reorder the terms: 3.214285715 + x = -2.983799797 Solving 3.214285715 + x = -2.983799797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.214285715' to each side of the equation. 3.214285715 + -3.214285715 + x = -2.983799797 + -3.214285715 Combine like terms: 3.214285715 + -3.214285715 = 0.000000000 0.000000000 + x = -2.983799797 + -3.214285715 x = -2.983799797 + -3.214285715 Combine like terms: -2.983799797 + -3.214285715 = -6.198085512 x = -6.198085512 Simplifying x = -6.198085512Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.230485918, -6.198085512}
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