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Simplifying 7x2 + -56x + 48 = 0 Reorder the terms: 48 + -56x + 7x2 = 0 Solving 48 + -56x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 6.857142857 + -8x + x2 = 0 Move the constant term to the right: Add '-6.857142857' to each side of the equation. 6.857142857 + -8x + -6.857142857 + x2 = 0 + -6.857142857 Reorder the terms: 6.857142857 + -6.857142857 + -8x + x2 = 0 + -6.857142857 Combine like terms: 6.857142857 + -6.857142857 = 0.000000000 0.000000000 + -8x + x2 = 0 + -6.857142857 -8x + x2 = 0 + -6.857142857 Combine like terms: 0 + -6.857142857 = -6.857142857 -8x + x2 = -6.857142857 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -6.857142857 + 16 Reorder the terms: 16 + -8x + x2 = -6.857142857 + 16 Combine like terms: -6.857142857 + 16 = 9.142857143 16 + -8x + x2 = 9.142857143 Factor a perfect square on the left side: (x + -4)(x + -4) = 9.142857143 Calculate the square root of the right side: 3.023715784 Break this problem into two subproblems by setting (x + -4) equal to 3.023715784 and -3.023715784.Subproblem 1
x + -4 = 3.023715784 Simplifying x + -4 = 3.023715784 Reorder the terms: -4 + x = 3.023715784 Solving -4 + x = 3.023715784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.023715784 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.023715784 + 4 x = 3.023715784 + 4 Combine like terms: 3.023715784 + 4 = 7.023715784 x = 7.023715784 Simplifying x = 7.023715784Subproblem 2
x + -4 = -3.023715784 Simplifying x + -4 = -3.023715784 Reorder the terms: -4 + x = -3.023715784 Solving -4 + x = -3.023715784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.023715784 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.023715784 + 4 x = -3.023715784 + 4 Combine like terms: -3.023715784 + 4 = 0.976284216 x = 0.976284216 Simplifying x = 0.976284216Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.023715784, 0.976284216}
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