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Simplifying x + 7x2 = 10 Solving x + 7x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + x + 7x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 0.1428571429x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 0.1428571429x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 0.1428571429x + x2 = 0 + 1.428571429 0.1428571429x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 0.1428571429x + x2 = 1.428571429 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1428571429x + 0.25 + x2 = 1.428571429 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = 1.428571429 + 0.25 Combine like terms: 1.428571429 + 0.25 = 1.678571429 0.25 + 0.1428571429x + x2 = 1.678571429 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.678571429 Calculate the square root of the right side: 1.295596939 Break this problem into two subproblems by setting (x + 0.5) equal to 1.295596939 and -1.295596939.Subproblem 1
x + 0.5 = 1.295596939 Simplifying x + 0.5 = 1.295596939 Reorder the terms: 0.5 + x = 1.295596939 Solving 0.5 + x = 1.295596939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.295596939 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.295596939 + -0.5 x = 1.295596939 + -0.5 Combine like terms: 1.295596939 + -0.5 = 0.795596939 x = 0.795596939 Simplifying x = 0.795596939Subproblem 2
x + 0.5 = -1.295596939 Simplifying x + 0.5 = -1.295596939 Reorder the terms: 0.5 + x = -1.295596939 Solving 0.5 + x = -1.295596939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.295596939 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.295596939 + -0.5 x = -1.295596939 + -0.5 Combine like terms: -1.295596939 + -0.5 = -1.795596939 x = -1.795596939 Simplifying x = -1.795596939Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.795596939, -1.795596939}
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