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Simplifying 4x2 + 56x + 93 = 0 Reorder the terms: 93 + 56x + 4x2 = 0 Solving 93 + 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'. 23.25 + 14x + x2 = 0 Move the constant term to the right: Add '-23.25' to each side of the equation. 23.25 + 14x + -23.25 + x2 = 0 + -23.25 Reorder the terms: 23.25 + -23.25 + 14x + x2 = 0 + -23.25 Combine like terms: 23.25 + -23.25 = 0.00 0.00 + 14x + x2 = 0 + -23.25 14x + x2 = 0 + -23.25 Combine like terms: 0 + -23.25 = -23.25 14x + x2 = -23.25 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 = -23.25 + 49 Reorder the terms: 49 + 14x + x2 = -23.25 + 49 Combine like terms: -23.25 + 49 = 25.75 49 + 14x + x2 = 25.75 Factor a perfect square on the left side: (x + 7)(x + 7) = 25.75 Calculate the square root of the right side: 5.074445783 Break this problem into two subproblems by setting (x + 7) equal to 5.074445783 and -5.074445783.Subproblem 1
x + 7 = 5.074445783 Simplifying x + 7 = 5.074445783 Reorder the terms: 7 + x = 5.074445783 Solving 7 + x = 5.074445783 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 = 5.074445783 + -7 Combine like terms: 7 + -7 = 0 0 + x = 5.074445783 + -7 x = 5.074445783 + -7 Combine like terms: 5.074445783 + -7 = -1.925554217 x = -1.925554217 Simplifying x = -1.925554217Subproblem 2
x + 7 = -5.074445783 Simplifying x + 7 = -5.074445783 Reorder the terms: 7 + x = -5.074445783 Solving 7 + x = -5.074445783 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 = -5.074445783 + -7 Combine like terms: 7 + -7 = 0 0 + x = -5.074445783 + -7 x = -5.074445783 + -7 Combine like terms: -5.074445783 + -7 = -12.074445783 x = -12.074445783 Simplifying x = -12.074445783Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.925554217, -12.074445783}
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