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Simplifying 7x2 + 3 + -17 = 47 + -45x Reorder the terms: 3 + -17 + 7x2 = 47 + -45x Combine like terms: 3 + -17 = -14 -14 + 7x2 = 47 + -45x Solving -14 + 7x2 = 47 + -45x Solving for variable 'x'. Reorder the terms: -14 + -47 + 45x + 7x2 = 47 + -45x + -47 + 45x Combine like terms: -14 + -47 = -61 -61 + 45x + 7x2 = 47 + -45x + -47 + 45x Reorder the terms: -61 + 45x + 7x2 = 47 + -47 + -45x + 45x Combine like terms: 47 + -47 = 0 -61 + 45x + 7x2 = 0 + -45x + 45x -61 + 45x + 7x2 = -45x + 45x Combine like terms: -45x + 45x = 0 -61 + 45x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -8.714285714 + 6.428571429x + x2 = 0 Move the constant term to the right: Add '8.714285714' to each side of the equation. -8.714285714 + 6.428571429x + 8.714285714 + x2 = 0 + 8.714285714 Reorder the terms: -8.714285714 + 8.714285714 + 6.428571429x + x2 = 0 + 8.714285714 Combine like terms: -8.714285714 + 8.714285714 = 0.000000000 0.000000000 + 6.428571429x + x2 = 0 + 8.714285714 6.428571429x + x2 = 0 + 8.714285714 Combine like terms: 0 + 8.714285714 = 8.714285714 6.428571429x + x2 = 8.714285714 The x term is 6.428571429x. Take half its coefficient (3.214285715). Square it (10.33163266) and add it to both sides. Add '10.33163266' to each side of the equation. 6.428571429x + 10.33163266 + x2 = 8.714285714 + 10.33163266 Reorder the terms: 10.33163266 + 6.428571429x + x2 = 8.714285714 + 10.33163266 Combine like terms: 8.714285714 + 10.33163266 = 19.045918374 10.33163266 + 6.428571429x + x2 = 19.045918374 Factor a perfect square on the left side: (x + 3.214285715)(x + 3.214285715) = 19.045918374 Calculate the square root of the right side: 4.364162964 Break this problem into two subproblems by setting (x + 3.214285715) equal to 4.364162964 and -4.364162964.Subproblem 1
x + 3.214285715 = 4.364162964 Simplifying x + 3.214285715 = 4.364162964 Reorder the terms: 3.214285715 + x = 4.364162964 Solving 3.214285715 + x = 4.364162964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.214285715' to each side of the equation. 3.214285715 + -3.214285715 + x = 4.364162964 + -3.214285715 Combine like terms: 3.214285715 + -3.214285715 = 0.000000000 0.000000000 + x = 4.364162964 + -3.214285715 x = 4.364162964 + -3.214285715 Combine like terms: 4.364162964 + -3.214285715 = 1.149877249 x = 1.149877249 Simplifying x = 1.149877249Subproblem 2
x + 3.214285715 = -4.364162964 Simplifying x + 3.214285715 = -4.364162964 Reorder the terms: 3.214285715 + x = -4.364162964 Solving 3.214285715 + x = -4.364162964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.214285715' to each side of the equation. 3.214285715 + -3.214285715 + x = -4.364162964 + -3.214285715 Combine like terms: 3.214285715 + -3.214285715 = 0.000000000 0.000000000 + x = -4.364162964 + -3.214285715 x = -4.364162964 + -3.214285715 Combine like terms: -4.364162964 + -3.214285715 = -7.578448679 x = -7.578448679 Simplifying x = -7.578448679Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.149877249, -7.578448679}
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