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Simplifying -1(14x * 4) + 7x2 = 160 Reorder the terms for easier multiplication: -1(14 * 4x) + 7x2 = 160 Multiply 14 * 4 -1(56x) + 7x2 = 160 Remove parenthesis around (56x) -1 * 56x + 7x2 = 160 Multiply -1 * 56 -56x + 7x2 = 160 Solving -56x + 7x2 = 160 Solving for variable 'x'. Reorder the terms: -160 + -56x + 7x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + -56x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -22.85714286 + -8x + x2 = 0 Move the constant term to the right: Add '22.85714286' to each side of the equation. -22.85714286 + -8x + 22.85714286 + x2 = 0 + 22.85714286 Reorder the terms: -22.85714286 + 22.85714286 + -8x + x2 = 0 + 22.85714286 Combine like terms: -22.85714286 + 22.85714286 = 0.00000000 0.00000000 + -8x + x2 = 0 + 22.85714286 -8x + x2 = 0 + 22.85714286 Combine like terms: 0 + 22.85714286 = 22.85714286 -8x + x2 = 22.85714286 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 = 22.85714286 + 16 Reorder the terms: 16 + -8x + x2 = 22.85714286 + 16 Combine like terms: 22.85714286 + 16 = 38.85714286 16 + -8x + x2 = 38.85714286 Factor a perfect square on the left side: (x + -4)(x + -4) = 38.85714286 Calculate the square root of the right side: 6.23354978 Break this problem into two subproblems by setting (x + -4) equal to 6.23354978 and -6.23354978.Subproblem 1
x + -4 = 6.23354978 Simplifying x + -4 = 6.23354978 Reorder the terms: -4 + x = 6.23354978 Solving -4 + x = 6.23354978 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 = 6.23354978 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.23354978 + 4 x = 6.23354978 + 4 Combine like terms: 6.23354978 + 4 = 10.23354978 x = 10.23354978 Simplifying x = 10.23354978Subproblem 2
x + -4 = -6.23354978 Simplifying x + -4 = -6.23354978 Reorder the terms: -4 + x = -6.23354978 Solving -4 + x = -6.23354978 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 = -6.23354978 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.23354978 + 4 x = -6.23354978 + 4 Combine like terms: -6.23354978 + 4 = -2.23354978 x = -2.23354978 Simplifying x = -2.23354978Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.23354978, -2.23354978}
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