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Simplifying -7 + -6x + -9 + 7x + -7x + 90x = 7x(3x) Reorder the terms: -7 + -9 + -6x + 7x + -7x + 90x = 7x(3x) Combine like terms: -7 + -9 = -16 -16 + -6x + 7x + -7x + 90x = 7x(3x) Combine like terms: -6x + 7x = 1x -16 + 1x + -7x + 90x = 7x(3x) Combine like terms: 1x + -7x = -6x -16 + -6x + 90x = 7x(3x) Combine like terms: -6x + 90x = 84x -16 + 84x = 7x(3x) Remove parenthesis around (3x) -16 + 84x = 7x * 3x Reorder the terms for easier multiplication: -16 + 84x = 7 * 3x * x Multiply 7 * 3 -16 + 84x = 21x * x Multiply x * x -16 + 84x = 21x2 Solving -16 + 84x = 21x2 Solving for variable 'x'. Combine like terms: 21x2 + -21x2 = 0 -16 + 84x + -21x2 = 0 Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. 0.7619047619 + -4x + x2 = 0 Move the constant term to the right: Add '-0.7619047619' to each side of the equation. 0.7619047619 + -4x + -0.7619047619 + x2 = 0 + -0.7619047619 Reorder the terms: 0.7619047619 + -0.7619047619 + -4x + x2 = 0 + -0.7619047619 Combine like terms: 0.7619047619 + -0.7619047619 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.7619047619 -4x + x2 = 0 + -0.7619047619 Combine like terms: 0 + -0.7619047619 = -0.7619047619 -4x + x2 = -0.7619047619 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.7619047619 + 4 Reorder the terms: 4 + -4x + x2 = -0.7619047619 + 4 Combine like terms: -0.7619047619 + 4 = 3.2380952381 4 + -4x + x2 = 3.2380952381 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.2380952381 Calculate the square root of the right side: 1.799470822 Break this problem into two subproblems by setting (x + -2) equal to 1.799470822 and -1.799470822.Subproblem 1
x + -2 = 1.799470822 Simplifying x + -2 = 1.799470822 Reorder the terms: -2 + x = 1.799470822 Solving -2 + x = 1.799470822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.799470822 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.799470822 + 2 x = 1.799470822 + 2 Combine like terms: 1.799470822 + 2 = 3.799470822 x = 3.799470822 Simplifying x = 3.799470822Subproblem 2
x + -2 = -1.799470822 Simplifying x + -2 = -1.799470822 Reorder the terms: -2 + x = -1.799470822 Solving -2 + x = -1.799470822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.799470822 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.799470822 + 2 x = -1.799470822 + 2 Combine like terms: -1.799470822 + 2 = 0.200529178 x = 0.200529178 Simplifying x = 0.200529178Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.799470822, 0.200529178}
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