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Simplifying 7x2 + -2x = 25 Reorder the terms: -2x + 7x2 = 25 Solving -2x + 7x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -2x + 7x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.571428571 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + -0.2857142857x + 3.571428571 + x2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + -0.2857142857x + x2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0 + 3.571428571 -0.2857142857x + x2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 -0.2857142857x + x2 = 3.571428571 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 = 3.571428571 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 3.571428571 + 0.02040816328 Combine like terms: 3.571428571 + 0.02040816328 = 3.59183673428 0.02040816328 + -0.2857142857x + x2 = 3.59183673428 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 3.59183673428 Calculate the square root of the right side: 1.895214166 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 1.895214166 and -1.895214166.Subproblem 1
x + -0.1428571429 = 1.895214166 Simplifying x + -0.1428571429 = 1.895214166 Reorder the terms: -0.1428571429 + x = 1.895214166 Solving -0.1428571429 + x = 1.895214166 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 = 1.895214166 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.895214166 + 0.1428571429 x = 1.895214166 + 0.1428571429 Combine like terms: 1.895214166 + 0.1428571429 = 2.0380713089 x = 2.0380713089 Simplifying x = 2.0380713089Subproblem 2
x + -0.1428571429 = -1.895214166 Simplifying x + -0.1428571429 = -1.895214166 Reorder the terms: -0.1428571429 + x = -1.895214166 Solving -0.1428571429 + x = -1.895214166 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 = -1.895214166 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.895214166 + 0.1428571429 x = -1.895214166 + 0.1428571429 Combine like terms: -1.895214166 + 0.1428571429 = -1.7523570231 x = -1.7523570231 Simplifying x = -1.7523570231Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0380713089, -1.7523570231}
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