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Simplifying 7x(x + -3) = x + 9 Reorder the terms: 7x(-3 + x) = x + 9 (-3 * 7x + x * 7x) = x + 9 (-21x + 7x2) = x + 9 Reorder the terms: -21x + 7x2 = 9 + x Solving -21x + 7x2 = 9 + x Solving for variable 'x'. Reorder the terms: -9 + -21x + -1x + 7x2 = 9 + x + -9 + -1x Combine like terms: -21x + -1x = -22x -9 + -22x + 7x2 = 9 + x + -9 + -1x Reorder the terms: -9 + -22x + 7x2 = 9 + -9 + x + -1x Combine like terms: 9 + -9 = 0 -9 + -22x + 7x2 = 0 + x + -1x -9 + -22x + 7x2 = x + -1x Combine like terms: x + -1x = 0 -9 + -22x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + -3.142857143x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -3.142857143x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -3.142857143x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -3.142857143x + x2 = 0 + 1.285714286 -3.142857143x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -3.142857143x + x2 = 1.285714286 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 = 1.285714286 + 2.469387757 Reorder the terms: 2.469387757 + -3.142857143x + x2 = 1.285714286 + 2.469387757 Combine like terms: 1.285714286 + 2.469387757 = 3.755102043 2.469387757 + -3.142857143x + x2 = 3.755102043 Factor a perfect square on the left side: (x + -1.571428572)(x + -1.571428572) = 3.755102043 Calculate the square root of the right side: 1.937808567 Break this problem into two subproblems by setting (x + -1.571428572) equal to 1.937808567 and -1.937808567.Subproblem 1
x + -1.571428572 = 1.937808567 Simplifying x + -1.571428572 = 1.937808567 Reorder the terms: -1.571428572 + x = 1.937808567 Solving -1.571428572 + x = 1.937808567 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 = 1.937808567 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + x = 1.937808567 + 1.571428572 x = 1.937808567 + 1.571428572 Combine like terms: 1.937808567 + 1.571428572 = 3.509237139 x = 3.509237139 Simplifying x = 3.509237139Subproblem 2
x + -1.571428572 = -1.937808567 Simplifying x + -1.571428572 = -1.937808567 Reorder the terms: -1.571428572 + x = -1.937808567 Solving -1.571428572 + x = -1.937808567 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 = -1.937808567 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + x = -1.937808567 + 1.571428572 x = -1.937808567 + 1.571428572 Combine like terms: -1.937808567 + 1.571428572 = -0.366379995 x = -0.366379995 Simplifying x = -0.366379995Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.509237139, -0.366379995}
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