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Simplifying 7x2 + -2x + -21 = 0 Reorder the terms: -21 + -2x + 7x2 = 0 Solving -21 + -2x + 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 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.2857142857x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.2857142857x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.2857142857x + x2 = 0 + 3 -0.2857142857x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.2857142857x + x2 = 3 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 = 3 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 3 + 0.02040816328 Combine like terms: 3 + 0.02040816328 = 3.02040816328 0.02040816328 + -0.2857142857x + x2 = 3.02040816328 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 3.02040816328 Calculate the square root of the right side: 1.737932152 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 1.737932152 and -1.737932152.Subproblem 1
x + -0.1428571429 = 1.737932152 Simplifying x + -0.1428571429 = 1.737932152 Reorder the terms: -0.1428571429 + x = 1.737932152 Solving -0.1428571429 + x = 1.737932152 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 = 1.737932152 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.737932152 + 0.1428571429 x = 1.737932152 + 0.1428571429 Combine like terms: 1.737932152 + 0.1428571429 = 1.8807892949 x = 1.8807892949 Simplifying x = 1.8807892949Subproblem 2
x + -0.1428571429 = -1.737932152 Simplifying x + -0.1428571429 = -1.737932152 Reorder the terms: -0.1428571429 + x = -1.737932152 Solving -0.1428571429 + x = -1.737932152 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 = -1.737932152 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.737932152 + 0.1428571429 x = -1.737932152 + 0.1428571429 Combine like terms: -1.737932152 + 0.1428571429 = -1.5950750091 x = -1.5950750091 Simplifying x = -1.5950750091Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8807892949, -1.5950750091}
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