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Simplifying 7x2 + -20x + -25 = 0 Reorder the terms: -25 + -20x + 7x2 = 0 Solving -25 + -20x + 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'. -3.571428571 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + -2.857142857x + 3.571428571 + x2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + -2.857142857x + x2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + -2.857142857x + x2 = 0 + 3.571428571 -2.857142857x + x2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 -2.857142857x + x2 = 3.571428571 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 3.571428571 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 3.571428571 + 2.040816328 Combine like terms: 3.571428571 + 2.040816328 = 5.612244899 2.040816328 + -2.857142857x + x2 = 5.612244899 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 5.612244899 Calculate the square root of the right side: 2.369017708 Break this problem into two subproblems by setting (x + -1.428571429) equal to 2.369017708 and -2.369017708.Subproblem 1
x + -1.428571429 = 2.369017708 Simplifying x + -1.428571429 = 2.369017708 Reorder the terms: -1.428571429 + x = 2.369017708 Solving -1.428571429 + x = 2.369017708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 2.369017708 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 2.369017708 + 1.428571429 x = 2.369017708 + 1.428571429 Combine like terms: 2.369017708 + 1.428571429 = 3.797589137 x = 3.797589137 Simplifying x = 3.797589137Subproblem 2
x + -1.428571429 = -2.369017708 Simplifying x + -1.428571429 = -2.369017708 Reorder the terms: -1.428571429 + x = -2.369017708 Solving -1.428571429 + x = -2.369017708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -2.369017708 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -2.369017708 + 1.428571429 x = -2.369017708 + 1.428571429 Combine like terms: -2.369017708 + 1.428571429 = -0.940446279 x = -0.940446279 Simplifying x = -0.940446279Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.797589137, -0.940446279}
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