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Simplifying 21x2 + -188x + -41 = 0 Reorder the terms: -41 + -188x + 21x2 = 0 Solving -41 + -188x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.952380952 + -8.952380952x + x2 = 0 Move the constant term to the right: Add '1.952380952' to each side of the equation. -1.952380952 + -8.952380952x + 1.952380952 + x2 = 0 + 1.952380952 Reorder the terms: -1.952380952 + 1.952380952 + -8.952380952x + x2 = 0 + 1.952380952 Combine like terms: -1.952380952 + 1.952380952 = 0.000000000 0.000000000 + -8.952380952x + x2 = 0 + 1.952380952 -8.952380952x + x2 = 0 + 1.952380952 Combine like terms: 0 + 1.952380952 = 1.952380952 -8.952380952x + x2 = 1.952380952 The x term is -8.952380952x. Take half its coefficient (-4.476190476). Square it (20.03628118) and add it to both sides. Add '20.03628118' to each side of the equation. -8.952380952x + 20.03628118 + x2 = 1.952380952 + 20.03628118 Reorder the terms: 20.03628118 + -8.952380952x + x2 = 1.952380952 + 20.03628118 Combine like terms: 1.952380952 + 20.03628118 = 21.988662132 20.03628118 + -8.952380952x + x2 = 21.988662132 Factor a perfect square on the left side: (x + -4.476190476)(x + -4.476190476) = 21.988662132 Calculate the square root of the right side: 4.689206983 Break this problem into two subproblems by setting (x + -4.476190476) equal to 4.689206983 and -4.689206983.Subproblem 1
x + -4.476190476 = 4.689206983 Simplifying x + -4.476190476 = 4.689206983 Reorder the terms: -4.476190476 + x = 4.689206983 Solving -4.476190476 + x = 4.689206983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.476190476' to each side of the equation. -4.476190476 + 4.476190476 + x = 4.689206983 + 4.476190476 Combine like terms: -4.476190476 + 4.476190476 = 0.000000000 0.000000000 + x = 4.689206983 + 4.476190476 x = 4.689206983 + 4.476190476 Combine like terms: 4.689206983 + 4.476190476 = 9.165397459 x = 9.165397459 Simplifying x = 9.165397459Subproblem 2
x + -4.476190476 = -4.689206983 Simplifying x + -4.476190476 = -4.689206983 Reorder the terms: -4.476190476 + x = -4.689206983 Solving -4.476190476 + x = -4.689206983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.476190476' to each side of the equation. -4.476190476 + 4.476190476 + x = -4.689206983 + 4.476190476 Combine like terms: -4.476190476 + 4.476190476 = 0.000000000 0.000000000 + x = -4.689206983 + 4.476190476 x = -4.689206983 + 4.476190476 Combine like terms: -4.689206983 + 4.476190476 = -0.213016507 x = -0.213016507 Simplifying x = -0.213016507Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.165397459, -0.213016507}
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