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Simplifying 7x2 + 22x + 4 = 7 Reorder the terms: 4 + 22x + 7x2 = 7 Solving 4 + 22x + 7x2 = 7 Solving for variable 'x'. Reorder the terms: 4 + -7 + 22x + 7x2 = 7 + -7 Combine like terms: 4 + -7 = -3 -3 + 22x + 7x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -3 + 22x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 3.142857143x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 3.142857143x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 3.142857143x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 3.142857143x + x2 = 0 + 0.4285714286 3.142857143x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 3.142857143x + x2 = 0.4285714286 The x term is 3.142857143x. Take half its coefficient (1.571428572). Square it (2.469387757) and add it to both sides. Add '2.469387757' to each side of the equation. 3.142857143x + 2.469387757 + x2 = 0.4285714286 + 2.469387757 Reorder the terms: 2.469387757 + 3.142857143x + x2 = 0.4285714286 + 2.469387757 Combine like terms: 0.4285714286 + 2.469387757 = 2.8979591856 2.469387757 + 3.142857143x + x2 = 2.8979591856 Factor a perfect square on the left side: (x + 1.571428572)(x + 1.571428572) = 2.8979591856 Calculate the square root of the right side: 1.702339327 Break this problem into two subproblems by setting (x + 1.571428572) equal to 1.702339327 and -1.702339327.Subproblem 1
x + 1.571428572 = 1.702339327 Simplifying x + 1.571428572 = 1.702339327 Reorder the terms: 1.571428572 + x = 1.702339327 Solving 1.571428572 + x = 1.702339327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = 1.702339327 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = 1.702339327 + -1.571428572 x = 1.702339327 + -1.571428572 Combine like terms: 1.702339327 + -1.571428572 = 0.130910755 x = 0.130910755 Simplifying x = 0.130910755Subproblem 2
x + 1.571428572 = -1.702339327 Simplifying x + 1.571428572 = -1.702339327 Reorder the terms: 1.571428572 + x = -1.702339327 Solving 1.571428572 + x = -1.702339327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = -1.702339327 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = -1.702339327 + -1.571428572 x = -1.702339327 + -1.571428572 Combine like terms: -1.702339327 + -1.571428572 = -3.273767899 x = -3.273767899 Simplifying x = -3.273767899Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.130910755, -3.273767899}
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