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Simplifying 7x2 + -2x + 1.68 = 210 Reorder the terms: 1.68 + -2x + 7x2 = 210 Solving 1.68 + -2x + 7x2 = 210 Solving for variable 'x'. Reorder the terms: 1.68 + -210 + -2x + 7x2 = 210 + -210 Combine like terms: 1.68 + -210 = -208.32 -208.32 + -2x + 7x2 = 210 + -210 Combine like terms: 210 + -210 = 0 -208.32 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -29.76 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '29.76' to each side of the equation. -29.76 + -0.2857142857x + 29.76 + x2 = 0 + 29.76 Reorder the terms: -29.76 + 29.76 + -0.2857142857x + x2 = 0 + 29.76 Combine like terms: -29.76 + 29.76 = 0.00 0.00 + -0.2857142857x + x2 = 0 + 29.76 -0.2857142857x + x2 = 0 + 29.76 Combine like terms: 0 + 29.76 = 29.76 -0.2857142857x + x2 = 29.76 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 = 29.76 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 29.76 + 0.02040816328 Combine like terms: 29.76 + 0.02040816328 = 29.78040816328 0.02040816328 + -0.2857142857x + x2 = 29.78040816328 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 29.78040816328 Calculate the square root of the right side: 5.457142857 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 5.457142857 and -5.457142857.Subproblem 1
x + -0.1428571429 = 5.457142857 Simplifying x + -0.1428571429 = 5.457142857 Reorder the terms: -0.1428571429 + x = 5.457142857 Solving -0.1428571429 + x = 5.457142857 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 = 5.457142857 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 5.457142857 + 0.1428571429 x = 5.457142857 + 0.1428571429 Combine like terms: 5.457142857 + 0.1428571429 = 5.5999999999 x = 5.5999999999 Simplifying x = 5.5999999999Subproblem 2
x + -0.1428571429 = -5.457142857 Simplifying x + -0.1428571429 = -5.457142857 Reorder the terms: -0.1428571429 + x = -5.457142857 Solving -0.1428571429 + x = -5.457142857 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 = -5.457142857 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -5.457142857 + 0.1428571429 x = -5.457142857 + 0.1428571429 Combine like terms: -5.457142857 + 0.1428571429 = -5.3142857141 x = -5.3142857141 Simplifying x = -5.3142857141Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5999999999, -5.3142857141}
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