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Simplifying 7x2 + 4x = 16 Reorder the terms: 4x + 7x2 = 16 Solving 4x + 7x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 4x + 7x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 0.5714285714x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 0.5714285714x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 0.5714285714x + x2 = 0 + 2.285714286 0.5714285714x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 0.5714285714x + x2 = 2.285714286 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 = 2.285714286 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 2.285714286 + 0.08163265305 Combine like terms: 2.285714286 + 0.08163265305 = 2.36734693905 0.08163265305 + 0.5714285714x + x2 = 2.36734693905 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 2.36734693905 Calculate the square root of the right side: 1.538618516 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 1.538618516 and -1.538618516.Subproblem 1
x + 0.2857142857 = 1.538618516 Simplifying x + 0.2857142857 = 1.538618516 Reorder the terms: 0.2857142857 + x = 1.538618516 Solving 0.2857142857 + x = 1.538618516 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 = 1.538618516 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 1.538618516 + -0.2857142857 x = 1.538618516 + -0.2857142857 Combine like terms: 1.538618516 + -0.2857142857 = 1.2529042303 x = 1.2529042303 Simplifying x = 1.2529042303Subproblem 2
x + 0.2857142857 = -1.538618516 Simplifying x + 0.2857142857 = -1.538618516 Reorder the terms: 0.2857142857 + x = -1.538618516 Solving 0.2857142857 + x = -1.538618516 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 = -1.538618516 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -1.538618516 + -0.2857142857 x = -1.538618516 + -0.2857142857 Combine like terms: -1.538618516 + -0.2857142857 = -1.8243328017 x = -1.8243328017 Simplifying x = -1.8243328017Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2529042303, -1.8243328017}
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