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Simplifying 7x2 + 17 + -24 = 12 + -2x Reorder the terms: 17 + -24 + 7x2 = 12 + -2x Combine like terms: 17 + -24 = -7 -7 + 7x2 = 12 + -2x Solving -7 + 7x2 = 12 + -2x Solving for variable 'x'. Reorder the terms: -7 + -12 + 2x + 7x2 = 12 + -2x + -12 + 2x Combine like terms: -7 + -12 = -19 -19 + 2x + 7x2 = 12 + -2x + -12 + 2x Reorder the terms: -19 + 2x + 7x2 = 12 + -12 + -2x + 2x Combine like terms: 12 + -12 = 0 -19 + 2x + 7x2 = 0 + -2x + 2x -19 + 2x + 7x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -19 + 2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.714285714 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '2.714285714' to each side of the equation. -2.714285714 + 0.2857142857x + 2.714285714 + x2 = 0 + 2.714285714 Reorder the terms: -2.714285714 + 2.714285714 + 0.2857142857x + x2 = 0 + 2.714285714 Combine like terms: -2.714285714 + 2.714285714 = 0.000000000 0.000000000 + 0.2857142857x + x2 = 0 + 2.714285714 0.2857142857x + x2 = 0 + 2.714285714 Combine like terms: 0 + 2.714285714 = 2.714285714 0.2857142857x + x2 = 2.714285714 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 = 2.714285714 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 2.714285714 + 0.02040816328 Combine like terms: 2.714285714 + 0.02040816328 = 2.73469387728 0.02040816328 + 0.2857142857x + x2 = 2.73469387728 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 2.73469387728 Calculate the square root of the right side: 1.653690986 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 1.653690986 and -1.653690986.Subproblem 1
x + 0.1428571429 = 1.653690986 Simplifying x + 0.1428571429 = 1.653690986 Reorder the terms: 0.1428571429 + x = 1.653690986 Solving 0.1428571429 + x = 1.653690986 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 = 1.653690986 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 1.653690986 + -0.1428571429 x = 1.653690986 + -0.1428571429 Combine like terms: 1.653690986 + -0.1428571429 = 1.5108338431 x = 1.5108338431 Simplifying x = 1.5108338431Subproblem 2
x + 0.1428571429 = -1.653690986 Simplifying x + 0.1428571429 = -1.653690986 Reorder the terms: 0.1428571429 + x = -1.653690986 Solving 0.1428571429 + x = -1.653690986 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 = -1.653690986 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -1.653690986 + -0.1428571429 x = -1.653690986 + -0.1428571429 Combine like terms: -1.653690986 + -0.1428571429 = -1.7965481289 x = -1.7965481289 Simplifying x = -1.7965481289Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5108338431, -1.7965481289}
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