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Simplifying 7x2 + -112x + 384 = 0 Reorder the terms: 384 + -112x + 7x2 = 0 Solving 384 + -112x + 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'. 54.85714286 + -16x + x2 = 0 Move the constant term to the right: Add '-54.85714286' to each side of the equation. 54.85714286 + -16x + -54.85714286 + x2 = 0 + -54.85714286 Reorder the terms: 54.85714286 + -54.85714286 + -16x + x2 = 0 + -54.85714286 Combine like terms: 54.85714286 + -54.85714286 = 0.00000000 0.00000000 + -16x + x2 = 0 + -54.85714286 -16x + x2 = 0 + -54.85714286 Combine like terms: 0 + -54.85714286 = -54.85714286 -16x + x2 = -54.85714286 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -54.85714286 + 64 Reorder the terms: 64 + -16x + x2 = -54.85714286 + 64 Combine like terms: -54.85714286 + 64 = 9.14285714 64 + -16x + x2 = 9.14285714 Factor a perfect square on the left side: (x + -8)(x + -8) = 9.14285714 Calculate the square root of the right side: 3.023715784 Break this problem into two subproblems by setting (x + -8) equal to 3.023715784 and -3.023715784.Subproblem 1
x + -8 = 3.023715784 Simplifying x + -8 = 3.023715784 Reorder the terms: -8 + x = 3.023715784 Solving -8 + x = 3.023715784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 3.023715784 + 8 Combine like terms: -8 + 8 = 0 0 + x = 3.023715784 + 8 x = 3.023715784 + 8 Combine like terms: 3.023715784 + 8 = 11.023715784 x = 11.023715784 Simplifying x = 11.023715784Subproblem 2
x + -8 = -3.023715784 Simplifying x + -8 = -3.023715784 Reorder the terms: -8 + x = -3.023715784 Solving -8 + x = -3.023715784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -3.023715784 + 8 Combine like terms: -8 + 8 = 0 0 + x = -3.023715784 + 8 x = -3.023715784 + 8 Combine like terms: -3.023715784 + 8 = 4.976284216 x = 4.976284216 Simplifying x = 4.976284216Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.023715784, 4.976284216}
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