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Simplifying 4x2 + -56x + 141 = 0 Reorder the terms: 141 + -56x + 4x2 = 0 Solving 141 + -56x + 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'. 35.25 + -14x + x2 = 0 Move the constant term to the right: Add '-35.25' to each side of the equation. 35.25 + -14x + -35.25 + x2 = 0 + -35.25 Reorder the terms: 35.25 + -35.25 + -14x + x2 = 0 + -35.25 Combine like terms: 35.25 + -35.25 = 0.00 0.00 + -14x + x2 = 0 + -35.25 -14x + x2 = 0 + -35.25 Combine like terms: 0 + -35.25 = -35.25 -14x + x2 = -35.25 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -35.25 + 49 Reorder the terms: 49 + -14x + x2 = -35.25 + 49 Combine like terms: -35.25 + 49 = 13.75 49 + -14x + x2 = 13.75 Factor a perfect square on the left side: (x + -7)(x + -7) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x + -7) equal to 3.708099244 and -3.708099244.Subproblem 1
x + -7 = 3.708099244 Simplifying x + -7 = 3.708099244 Reorder the terms: -7 + x = 3.708099244 Solving -7 + x = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 3.708099244 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.708099244 + 7 x = 3.708099244 + 7 Combine like terms: 3.708099244 + 7 = 10.708099244 x = 10.708099244 Simplifying x = 10.708099244Subproblem 2
x + -7 = -3.708099244 Simplifying x + -7 = -3.708099244 Reorder the terms: -7 + x = -3.708099244 Solving -7 + x = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -3.708099244 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.708099244 + 7 x = -3.708099244 + 7 Combine like terms: -3.708099244 + 7 = 3.291900756 x = 3.291900756 Simplifying x = 3.291900756Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.708099244, 3.291900756}
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