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Simplifying 7x2 + -2x + 21 = 26x + 1 Reorder the terms: 21 + -2x + 7x2 = 26x + 1 Reorder the terms: 21 + -2x + 7x2 = 1 + 26x Solving 21 + -2x + 7x2 = 1 + 26x Solving for variable 'x'. Reorder the terms: 21 + -1 + -2x + -26x + 7x2 = 1 + 26x + -1 + -26x Combine like terms: 21 + -1 = 20 20 + -2x + -26x + 7x2 = 1 + 26x + -1 + -26x Combine like terms: -2x + -26x = -28x 20 + -28x + 7x2 = 1 + 26x + -1 + -26x Reorder the terms: 20 + -28x + 7x2 = 1 + -1 + 26x + -26x Combine like terms: 1 + -1 = 0 20 + -28x + 7x2 = 0 + 26x + -26x 20 + -28x + 7x2 = 26x + -26x Combine like terms: 26x + -26x = 0 20 + -28x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.857142857 + -4x + x2 = 0 Move the constant term to the right: Add '-2.857142857' to each side of the equation. 2.857142857 + -4x + -2.857142857 + x2 = 0 + -2.857142857 Reorder the terms: 2.857142857 + -2.857142857 + -4x + x2 = 0 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + -4x + x2 = 0 + -2.857142857 -4x + x2 = 0 + -2.857142857 Combine like terms: 0 + -2.857142857 = -2.857142857 -4x + x2 = -2.857142857 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 = -2.857142857 + 4 Reorder the terms: 4 + -4x + x2 = -2.857142857 + 4 Combine like terms: -2.857142857 + 4 = 1.142857143 4 + -4x + x2 = 1.142857143 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.142857143 Calculate the square root of the right side: 1.069044968 Break this problem into two subproblems by setting (x + -2) equal to 1.069044968 and -1.069044968.Subproblem 1
x + -2 = 1.069044968 Simplifying x + -2 = 1.069044968 Reorder the terms: -2 + x = 1.069044968 Solving -2 + x = 1.069044968 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 = 1.069044968 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.069044968 + 2 x = 1.069044968 + 2 Combine like terms: 1.069044968 + 2 = 3.069044968 x = 3.069044968 Simplifying x = 3.069044968Subproblem 2
x + -2 = -1.069044968 Simplifying x + -2 = -1.069044968 Reorder the terms: -2 + x = -1.069044968 Solving -2 + x = -1.069044968 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 = -1.069044968 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.069044968 + 2 x = -1.069044968 + 2 Combine like terms: -1.069044968 + 2 = 0.930955032 x = 0.930955032 Simplifying x = 0.930955032Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.069044968, 0.930955032}
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