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Simplifying 4x2 + -56x + 105 = 0 Reorder the terms: 105 + -56x + 4x2 = 0 Solving 105 + -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'. 26.25 + -14x + x2 = 0 Move the constant term to the right: Add '-26.25' to each side of the equation. 26.25 + -14x + -26.25 + x2 = 0 + -26.25 Reorder the terms: 26.25 + -26.25 + -14x + x2 = 0 + -26.25 Combine like terms: 26.25 + -26.25 = 0.00 0.00 + -14x + x2 = 0 + -26.25 -14x + x2 = 0 + -26.25 Combine like terms: 0 + -26.25 = -26.25 -14x + x2 = -26.25 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 = -26.25 + 49 Reorder the terms: 49 + -14x + x2 = -26.25 + 49 Combine like terms: -26.25 + 49 = 22.75 49 + -14x + x2 = 22.75 Factor a perfect square on the left side: (x + -7)(x + -7) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (x + -7) equal to 4.769696007 and -4.769696007.Subproblem 1
x + -7 = 4.769696007 Simplifying x + -7 = 4.769696007 Reorder the terms: -7 + x = 4.769696007 Solving -7 + x = 4.769696007 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 = 4.769696007 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.769696007 + 7 x = 4.769696007 + 7 Combine like terms: 4.769696007 + 7 = 11.769696007 x = 11.769696007 Simplifying x = 11.769696007Subproblem 2
x + -7 = -4.769696007 Simplifying x + -7 = -4.769696007 Reorder the terms: -7 + x = -4.769696007 Solving -7 + x = -4.769696007 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 = -4.769696007 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.769696007 + 7 x = -4.769696007 + 7 Combine like terms: -4.769696007 + 7 = 2.230303993 x = 2.230303993 Simplifying x = 2.230303993Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.769696007, 2.230303993}
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