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Simplifying 4x2 + 56x + -99 = 0 Reorder the terms: -99 + 56x + 4x2 = 0 Solving -99 + 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'. -24.75 + 14x + x2 = 0 Move the constant term to the right: Add '24.75' to each side of the equation. -24.75 + 14x + 24.75 + x2 = 0 + 24.75 Reorder the terms: -24.75 + 24.75 + 14x + x2 = 0 + 24.75 Combine like terms: -24.75 + 24.75 = 0.00 0.00 + 14x + x2 = 0 + 24.75 14x + x2 = 0 + 24.75 Combine like terms: 0 + 24.75 = 24.75 14x + x2 = 24.75 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 = 24.75 + 49 Reorder the terms: 49 + 14x + x2 = 24.75 + 49 Combine like terms: 24.75 + 49 = 73.75 49 + 14x + x2 = 73.75 Factor a perfect square on the left side: (x + 7)(x + 7) = 73.75 Calculate the square root of the right side: 8.587782019 Break this problem into two subproblems by setting (x + 7) equal to 8.587782019 and -8.587782019.Subproblem 1
x + 7 = 8.587782019 Simplifying x + 7 = 8.587782019 Reorder the terms: 7 + x = 8.587782019 Solving 7 + x = 8.587782019 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 = 8.587782019 + -7 Combine like terms: 7 + -7 = 0 0 + x = 8.587782019 + -7 x = 8.587782019 + -7 Combine like terms: 8.587782019 + -7 = 1.587782019 x = 1.587782019 Simplifying x = 1.587782019Subproblem 2
x + 7 = -8.587782019 Simplifying x + 7 = -8.587782019 Reorder the terms: 7 + x = -8.587782019 Solving 7 + x = -8.587782019 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 = -8.587782019 + -7 Combine like terms: 7 + -7 = 0 0 + x = -8.587782019 + -7 x = -8.587782019 + -7 Combine like terms: -8.587782019 + -7 = -15.587782019 x = -15.587782019 Simplifying x = -15.587782019Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.587782019, -15.587782019}
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