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Simplifying 7x2 + -14x = 57 Reorder the terms: -14x + 7x2 = 57 Solving -14x + 7x2 = 57 Solving for variable 'x'. Reorder the terms: -57 + -14x + 7x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + -14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -8.142857143 + -2x + x2 = 0 Move the constant term to the right: Add '8.142857143' to each side of the equation. -8.142857143 + -2x + 8.142857143 + x2 = 0 + 8.142857143 Reorder the terms: -8.142857143 + 8.142857143 + -2x + x2 = 0 + 8.142857143 Combine like terms: -8.142857143 + 8.142857143 = 0.000000000 0.000000000 + -2x + x2 = 0 + 8.142857143 -2x + x2 = 0 + 8.142857143 Combine like terms: 0 + 8.142857143 = 8.142857143 -2x + x2 = 8.142857143 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 8.142857143 + 1 Reorder the terms: 1 + -2x + x2 = 8.142857143 + 1 Combine like terms: 8.142857143 + 1 = 9.142857143 1 + -2x + x2 = 9.142857143 Factor a perfect square on the left side: (x + -1)(x + -1) = 9.142857143 Calculate the square root of the right side: 3.023715784 Break this problem into two subproblems by setting (x + -1) equal to 3.023715784 and -3.023715784.Subproblem 1
x + -1 = 3.023715784 Simplifying x + -1 = 3.023715784 Reorder the terms: -1 + x = 3.023715784 Solving -1 + x = 3.023715784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.023715784 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.023715784 + 1 x = 3.023715784 + 1 Combine like terms: 3.023715784 + 1 = 4.023715784 x = 4.023715784 Simplifying x = 4.023715784Subproblem 2
x + -1 = -3.023715784 Simplifying x + -1 = -3.023715784 Reorder the terms: -1 + x = -3.023715784 Solving -1 + x = -3.023715784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.023715784 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.023715784 + 1 x = -3.023715784 + 1 Combine like terms: -3.023715784 + 1 = -2.023715784 x = -2.023715784 Simplifying x = -2.023715784Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.023715784, -2.023715784}
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