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Simplifying 7x2 + -2x + -6 = 7 Reorder the terms: -6 + -2x + 7x2 = 7 Solving -6 + -2x + 7x2 = 7 Solving for variable 'x'. Reorder the terms: -6 + -7 + -2x + 7x2 = 7 + -7 Combine like terms: -6 + -7 = -13 -13 + -2x + 7x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -13 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + -0.2857142857x + 1.857142857 + x2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + -0.2857142857x + x2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0 + 1.857142857 -0.2857142857x + x2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 -0.2857142857x + x2 = 1.857142857 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 = 1.857142857 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 1.857142857 + 0.02040816328 Combine like terms: 1.857142857 + 0.02040816328 = 1.87755102028 0.02040816328 + -0.2857142857x + x2 = 1.87755102028 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 1.87755102028 Calculate the square root of the right side: 1.370237578 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 1.370237578 and -1.370237578.Subproblem 1
x + -0.1428571429 = 1.370237578 Simplifying x + -0.1428571429 = 1.370237578 Reorder the terms: -0.1428571429 + x = 1.370237578 Solving -0.1428571429 + x = 1.370237578 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 = 1.370237578 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.370237578 + 0.1428571429 x = 1.370237578 + 0.1428571429 Combine like terms: 1.370237578 + 0.1428571429 = 1.5130947209 x = 1.5130947209 Simplifying x = 1.5130947209Subproblem 2
x + -0.1428571429 = -1.370237578 Simplifying x + -0.1428571429 = -1.370237578 Reorder the terms: -0.1428571429 + x = -1.370237578 Solving -0.1428571429 + x = -1.370237578 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 = -1.370237578 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.370237578 + 0.1428571429 x = -1.370237578 + 0.1428571429 Combine like terms: -1.370237578 + 0.1428571429 = -1.2273804351 x = -1.2273804351 Simplifying x = -1.2273804351Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5130947209, -1.2273804351}
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