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Simplifying 7x2 + 3x = 35 Reorder the terms: 3x + 7x2 = 35 Solving 3x + 7x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 3x + 7x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.4285714286x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.4285714286x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.4285714286x + x2 = 0 + 5 0.4285714286x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.4285714286x + x2 = 5 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 5 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 5 + 0.04591836735 Combine like terms: 5 + 0.04591836735 = 5.04591836735 0.04591836735 + 0.4285714286x + x2 = 5.04591836735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 5.04591836735 Calculate the square root of the right side: 2.246312171 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 2.246312171 and -2.246312171.Subproblem 1
x + 0.2142857143 = 2.246312171 Simplifying x + 0.2142857143 = 2.246312171 Reorder the terms: 0.2142857143 + x = 2.246312171 Solving 0.2142857143 + x = 2.246312171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 2.246312171 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 2.246312171 + -0.2142857143 x = 2.246312171 + -0.2142857143 Combine like terms: 2.246312171 + -0.2142857143 = 2.0320264567 x = 2.0320264567 Simplifying x = 2.0320264567Subproblem 2
x + 0.2142857143 = -2.246312171 Simplifying x + 0.2142857143 = -2.246312171 Reorder the terms: 0.2142857143 + x = -2.246312171 Solving 0.2142857143 + x = -2.246312171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -2.246312171 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -2.246312171 + -0.2142857143 x = -2.246312171 + -0.2142857143 Combine like terms: -2.246312171 + -0.2142857143 = -2.4605978853 x = -2.4605978853 Simplifying x = -2.4605978853Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0320264567, -2.4605978853}
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