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Simplifying 4x2 + -56x + 3 = 0 Reorder the terms: 3 + -56x + 4x2 = 0 Solving 3 + -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'. 0.75 + -14x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -14x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -14x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -14x + x2 = 0 + -0.75 -14x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -14x + x2 = -0.75 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 = -0.75 + 49 Reorder the terms: 49 + -14x + x2 = -0.75 + 49 Combine like terms: -0.75 + 49 = 48.25 49 + -14x + x2 = 48.25 Factor a perfect square on the left side: (x + -7)(x + -7) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + -7) equal to 6.946221995 and -6.946221995.Subproblem 1
x + -7 = 6.946221995 Simplifying x + -7 = 6.946221995 Reorder the terms: -7 + x = 6.946221995 Solving -7 + x = 6.946221995 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 = 6.946221995 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.946221995 + 7 x = 6.946221995 + 7 Combine like terms: 6.946221995 + 7 = 13.946221995 x = 13.946221995 Simplifying x = 13.946221995Subproblem 2
x + -7 = -6.946221995 Simplifying x + -7 = -6.946221995 Reorder the terms: -7 + x = -6.946221995 Solving -7 + x = -6.946221995 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 = -6.946221995 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.946221995 + 7 x = -6.946221995 + 7 Combine like terms: -6.946221995 + 7 = 0.053778005 x = 0.053778005 Simplifying x = 0.053778005Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.946221995, 0.053778005}
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