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Simplifying 4x2 + -56x + -313 = 0 Reorder the terms: -313 + -56x + 4x2 = 0 Solving -313 + -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'. -78.25 + -14x + x2 = 0 Move the constant term to the right: Add '78.25' to each side of the equation. -78.25 + -14x + 78.25 + x2 = 0 + 78.25 Reorder the terms: -78.25 + 78.25 + -14x + x2 = 0 + 78.25 Combine like terms: -78.25 + 78.25 = 0.00 0.00 + -14x + x2 = 0 + 78.25 -14x + x2 = 0 + 78.25 Combine like terms: 0 + 78.25 = 78.25 -14x + x2 = 78.25 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 = 78.25 + 49 Reorder the terms: 49 + -14x + x2 = 78.25 + 49 Combine like terms: 78.25 + 49 = 127.25 49 + -14x + x2 = 127.25 Factor a perfect square on the left side: (x + -7)(x + -7) = 127.25 Calculate the square root of the right side: 11.280514173 Break this problem into two subproblems by setting (x + -7) equal to 11.280514173 and -11.280514173.Subproblem 1
x + -7 = 11.280514173 Simplifying x + -7 = 11.280514173 Reorder the terms: -7 + x = 11.280514173 Solving -7 + x = 11.280514173 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 = 11.280514173 + 7 Combine like terms: -7 + 7 = 0 0 + x = 11.280514173 + 7 x = 11.280514173 + 7 Combine like terms: 11.280514173 + 7 = 18.280514173 x = 18.280514173 Simplifying x = 18.280514173Subproblem 2
x + -7 = -11.280514173 Simplifying x + -7 = -11.280514173 Reorder the terms: -7 + x = -11.280514173 Solving -7 + x = -11.280514173 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 = -11.280514173 + 7 Combine like terms: -7 + 7 = 0 0 + x = -11.280514173 + 7 x = -11.280514173 + 7 Combine like terms: -11.280514173 + 7 = -4.280514173 x = -4.280514173 Simplifying x = -4.280514173Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.280514173, -4.280514173}
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