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Simplifying 7x2 + 3x + 5 = 21 Reorder the terms: 5 + 3x + 7x2 = 21 Solving 5 + 3x + 7x2 = 21 Solving for variable 'x'. Reorder the terms: 5 + -21 + 3x + 7x2 = 21 + -21 Combine like terms: 5 + -21 = -16 -16 + 3x + 7x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -16 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 0.4285714286x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 0.4285714286x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + 2.285714286 0.4285714286x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 0.4285714286x + x2 = 2.285714286 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 = 2.285714286 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 2.285714286 + 0.04591836735 Combine like terms: 2.285714286 + 0.04591836735 = 2.33163265335 0.04591836735 + 0.4285714286x + x2 = 2.33163265335 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 2.33163265335 Calculate the square root of the right side: 1.526968452 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.526968452 and -1.526968452.Subproblem 1
x + 0.2142857143 = 1.526968452 Simplifying x + 0.2142857143 = 1.526968452 Reorder the terms: 0.2142857143 + x = 1.526968452 Solving 0.2142857143 + x = 1.526968452 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 = 1.526968452 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.526968452 + -0.2142857143 x = 1.526968452 + -0.2142857143 Combine like terms: 1.526968452 + -0.2142857143 = 1.3126827377 x = 1.3126827377 Simplifying x = 1.3126827377Subproblem 2
x + 0.2142857143 = -1.526968452 Simplifying x + 0.2142857143 = -1.526968452 Reorder the terms: 0.2142857143 + x = -1.526968452 Solving 0.2142857143 + x = -1.526968452 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 = -1.526968452 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.526968452 + -0.2142857143 x = -1.526968452 + -0.2142857143 Combine like terms: -1.526968452 + -0.2142857143 = -1.7412541663 x = -1.7412541663 Simplifying x = -1.7412541663Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3126827377, -1.7412541663}
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