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Simplifying x2 + -3x + 5 * 4x2 + -3x + -2 = 0 Multiply 5 * 4 x2 + -3x + 20x2 + -3x + -2 = 0 Reorder the terms: -2 + -3x + -3x + x2 + 20x2 = 0 Combine like terms: -3x + -3x = -6x -2 + -6x + x2 + 20x2 = 0 Combine like terms: x2 + 20x2 = 21x2 -2 + -6x + 21x2 = 0 Solving -2 + -6x + 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'. -0.09523809524 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.09523809524' to each side of the equation. -0.09523809524 + -0.2857142857x + 0.09523809524 + x2 = 0 + 0.09523809524 Reorder the terms: -0.09523809524 + 0.09523809524 + -0.2857142857x + x2 = 0 + 0.09523809524 Combine like terms: -0.09523809524 + 0.09523809524 = 0.00000000000 0.00000000000 + -0.2857142857x + x2 = 0 + 0.09523809524 -0.2857142857x + x2 = 0 + 0.09523809524 Combine like terms: 0 + 0.09523809524 = 0.09523809524 -0.2857142857x + x2 = 0.09523809524 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 0.09523809524 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.09523809524 + 0.02040816328 Combine like terms: 0.09523809524 + 0.02040816328 = 0.11564625852 0.02040816328 + -0.2857142857x + x2 = 0.11564625852 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.11564625852 Calculate the square root of the right side: 0.34006802 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.34006802 and -0.34006802.Subproblem 1
x + -0.1428571429 = 0.34006802 Simplifying x + -0.1428571429 = 0.34006802 Reorder the terms: -0.1428571429 + x = 0.34006802 Solving -0.1428571429 + x = 0.34006802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.34006802 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.34006802 + 0.1428571429 x = 0.34006802 + 0.1428571429 Combine like terms: 0.34006802 + 0.1428571429 = 0.4829251629 x = 0.4829251629 Simplifying x = 0.4829251629Subproblem 2
x + -0.1428571429 = -0.34006802 Simplifying x + -0.1428571429 = -0.34006802 Reorder the terms: -0.1428571429 + x = -0.34006802 Solving -0.1428571429 + x = -0.34006802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.34006802 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.34006802 + 0.1428571429 x = -0.34006802 + 0.1428571429 Combine like terms: -0.34006802 + 0.1428571429 = -0.1972108771 x = -0.1972108771 Simplifying x = -0.1972108771Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4829251629, -0.1972108771}
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