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Simplifying 7x2 + 4x = 173 Reorder the terms: 4x + 7x2 = 173 Solving 4x + 7x2 = 173 Solving for variable 'x'. Reorder the terms: -173 + 4x + 7x2 = 173 + -173 Combine like terms: 173 + -173 = 0 -173 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -24.71428571 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '24.71428571' to each side of the equation. -24.71428571 + 0.5714285714x + 24.71428571 + x2 = 0 + 24.71428571 Reorder the terms: -24.71428571 + 24.71428571 + 0.5714285714x + x2 = 0 + 24.71428571 Combine like terms: -24.71428571 + 24.71428571 = 0.00000000 0.00000000 + 0.5714285714x + x2 = 0 + 24.71428571 0.5714285714x + x2 = 0 + 24.71428571 Combine like terms: 0 + 24.71428571 = 24.71428571 0.5714285714x + x2 = 24.71428571 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 24.71428571 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 24.71428571 + 0.08163265305 Combine like terms: 24.71428571 + 0.08163265305 = 24.79591836305 0.08163265305 + 0.5714285714x + x2 = 24.79591836305 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 24.79591836305 Calculate the square root of the right side: 4.979550016 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 4.979550016 and -4.979550016.Subproblem 1
x + 0.2857142857 = 4.979550016 Simplifying x + 0.2857142857 = 4.979550016 Reorder the terms: 0.2857142857 + x = 4.979550016 Solving 0.2857142857 + x = 4.979550016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 4.979550016 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 4.979550016 + -0.2857142857 x = 4.979550016 + -0.2857142857 Combine like terms: 4.979550016 + -0.2857142857 = 4.6938357303 x = 4.6938357303 Simplifying x = 4.6938357303Subproblem 2
x + 0.2857142857 = -4.979550016 Simplifying x + 0.2857142857 = -4.979550016 Reorder the terms: 0.2857142857 + x = -4.979550016 Solving 0.2857142857 + x = -4.979550016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -4.979550016 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -4.979550016 + -0.2857142857 x = -4.979550016 + -0.2857142857 Combine like terms: -4.979550016 + -0.2857142857 = -5.2652643017 x = -5.2652643017 Simplifying x = -5.2652643017Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.6938357303, -5.2652643017}
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