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Simplifying 4x2 + -112x + -343 = 0 Reorder the terms: -343 + -112x + 4x2 = 0 Solving -343 + -112x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -85.75 + -28x + x2 = 0 Move the constant term to the right: Add '85.75' to each side of the equation. -85.75 + -28x + 85.75 + x2 = 0 + 85.75 Reorder the terms: -85.75 + 85.75 + -28x + x2 = 0 + 85.75 Combine like terms: -85.75 + 85.75 = 0.00 0.00 + -28x + x2 = 0 + 85.75 -28x + x2 = 0 + 85.75 Combine like terms: 0 + 85.75 = 85.75 -28x + x2 = 85.75 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = 85.75 + 196 Reorder the terms: 196 + -28x + x2 = 85.75 + 196 Combine like terms: 85.75 + 196 = 281.75 196 + -28x + x2 = 281.75 Factor a perfect square on the left side: (x + -14)(x + -14) = 281.75 Calculate the square root of the right side: 16.785410332 Break this problem into two subproblems by setting (x + -14) equal to 16.785410332 and -16.785410332.Subproblem 1
x + -14 = 16.785410332 Simplifying x + -14 = 16.785410332 Reorder the terms: -14 + x = 16.785410332 Solving -14 + x = 16.785410332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 16.785410332 + 14 Combine like terms: -14 + 14 = 0 0 + x = 16.785410332 + 14 x = 16.785410332 + 14 Combine like terms: 16.785410332 + 14 = 30.785410332 x = 30.785410332 Simplifying x = 30.785410332Subproblem 2
x + -14 = -16.785410332 Simplifying x + -14 = -16.785410332 Reorder the terms: -14 + x = -16.785410332 Solving -14 + x = -16.785410332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -16.785410332 + 14 Combine like terms: -14 + 14 = 0 0 + x = -16.785410332 + 14 x = -16.785410332 + 14 Combine like terms: -16.785410332 + 14 = -2.785410332 x = -2.785410332 Simplifying x = -2.785410332Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.785410332, -2.785410332}
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