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Simplifying 7x2 + -2x + -14 = 21 Reorder the terms: -14 + -2x + 7x2 = 21 Solving -14 + -2x + 7x2 = 21 Solving for variable 'x'. Reorder the terms: -14 + -21 + -2x + 7x2 = 21 + -21 Combine like terms: -14 + -21 = -35 -35 + -2x + 7x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -35 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.2857142857x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.2857142857x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.2857142857x + x2 = 0 + 5 -0.2857142857x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.2857142857x + x2 = 5 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 = 5 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 5 + 0.02040816328 Combine like terms: 5 + 0.02040816328 = 5.02040816328 0.02040816328 + -0.2857142857x + x2 = 5.02040816328 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 5.02040816328 Calculate the square root of the right side: 2.240626734 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 2.240626734 and -2.240626734.Subproblem 1
x + -0.1428571429 = 2.240626734 Simplifying x + -0.1428571429 = 2.240626734 Reorder the terms: -0.1428571429 + x = 2.240626734 Solving -0.1428571429 + x = 2.240626734 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 = 2.240626734 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 2.240626734 + 0.1428571429 x = 2.240626734 + 0.1428571429 Combine like terms: 2.240626734 + 0.1428571429 = 2.3834838769 x = 2.3834838769 Simplifying x = 2.3834838769Subproblem 2
x + -0.1428571429 = -2.240626734 Simplifying x + -0.1428571429 = -2.240626734 Reorder the terms: -0.1428571429 + x = -2.240626734 Solving -0.1428571429 + x = -2.240626734 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 = -2.240626734 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -2.240626734 + 0.1428571429 x = -2.240626734 + 0.1428571429 Combine like terms: -2.240626734 + 0.1428571429 = -2.0977695911 x = -2.0977695911 Simplifying x = -2.0977695911Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3834838769, -2.0977695911}
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