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Simplifying 5 + 2x = 7x2 + -7 Reorder the terms: 5 + 2x = -7 + 7x2 Solving 5 + 2x = -7 + 7x2 Solving for variable 'x'. Reorder the terms: 5 + 7 + 2x + -7x2 = -7 + 7x2 + 7 + -7x2 Combine like terms: 5 + 7 = 12 12 + 2x + -7x2 = -7 + 7x2 + 7 + -7x2 Reorder the terms: 12 + 2x + -7x2 = -7 + 7 + 7x2 + -7x2 Combine like terms: -7 + 7 = 0 12 + 2x + -7x2 = 0 + 7x2 + -7x2 12 + 2x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 12 + 2x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.714285714 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -0.2857142857x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -0.2857142857x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0 + 1.714285714 -0.2857142857x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -0.2857142857x + x2 = 1.714285714 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 = 1.714285714 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 1.714285714 + 0.02040816328 Combine like terms: 1.714285714 + 0.02040816328 = 1.73469387728 0.02040816328 + -0.2857142857x + x2 = 1.73469387728 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 1.73469387728 Calculate the square root of the right side: 1.31707778 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 1.31707778 and -1.31707778.Subproblem 1
x + -0.1428571429 = 1.31707778 Simplifying x + -0.1428571429 = 1.31707778 Reorder the terms: -0.1428571429 + x = 1.31707778 Solving -0.1428571429 + x = 1.31707778 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 = 1.31707778 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.31707778 + 0.1428571429 x = 1.31707778 + 0.1428571429 Combine like terms: 1.31707778 + 0.1428571429 = 1.4599349229 x = 1.4599349229 Simplifying x = 1.4599349229Subproblem 2
x + -0.1428571429 = -1.31707778 Simplifying x + -0.1428571429 = -1.31707778 Reorder the terms: -0.1428571429 + x = -1.31707778 Solving -0.1428571429 + x = -1.31707778 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 = -1.31707778 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.31707778 + 0.1428571429 x = -1.31707778 + 0.1428571429 Combine like terms: -1.31707778 + 0.1428571429 = -1.1742206371 x = -1.1742206371 Simplifying x = -1.1742206371Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4599349229, -1.1742206371}
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