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Simplifying 7x2 + -28x + 17 = -7 Reorder the terms: 17 + -28x + 7x2 = -7 Solving 17 + -28x + 7x2 = -7 Solving for variable 'x'. Reorder the terms: 17 + 7 + -28x + 7x2 = -7 + 7 Combine like terms: 17 + 7 = 24 24 + -28x + 7x2 = -7 + 7 Combine like terms: -7 + 7 = 0 24 + -28x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.428571429 + -4x + x2 = 0 Move the constant term to the right: Add '-3.428571429' to each side of the equation. 3.428571429 + -4x + -3.428571429 + x2 = 0 + -3.428571429 Reorder the terms: 3.428571429 + -3.428571429 + -4x + x2 = 0 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + -4x + x2 = 0 + -3.428571429 -4x + x2 = 0 + -3.428571429 Combine like terms: 0 + -3.428571429 = -3.428571429 -4x + x2 = -3.428571429 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 = -3.428571429 + 4 Reorder the terms: 4 + -4x + x2 = -3.428571429 + 4 Combine like terms: -3.428571429 + 4 = 0.571428571 4 + -4x + x2 = 0.571428571 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.571428571 Calculate the square root of the right side: 0.755928946 Break this problem into two subproblems by setting (x + -2) equal to 0.755928946 and -0.755928946.Subproblem 1
x + -2 = 0.755928946 Simplifying x + -2 = 0.755928946 Reorder the terms: -2 + x = 0.755928946 Solving -2 + x = 0.755928946 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 = 0.755928946 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.755928946 + 2 x = 0.755928946 + 2 Combine like terms: 0.755928946 + 2 = 2.755928946 x = 2.755928946 Simplifying x = 2.755928946Subproblem 2
x + -2 = -0.755928946 Simplifying x + -2 = -0.755928946 Reorder the terms: -2 + x = -0.755928946 Solving -2 + x = -0.755928946 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 = -0.755928946 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.755928946 + 2 x = -0.755928946 + 2 Combine like terms: -0.755928946 + 2 = 1.244071054 x = 1.244071054 Simplifying x = 1.244071054Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.755928946, 1.244071054}
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