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Simplifying 4x2 + 56x + 185 = 0 Reorder the terms: 185 + 56x + 4x2 = 0 Solving 185 + 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'. 46.25 + 14x + x2 = 0 Move the constant term to the right: Add '-46.25' to each side of the equation. 46.25 + 14x + -46.25 + x2 = 0 + -46.25 Reorder the terms: 46.25 + -46.25 + 14x + x2 = 0 + -46.25 Combine like terms: 46.25 + -46.25 = 0.00 0.00 + 14x + x2 = 0 + -46.25 14x + x2 = 0 + -46.25 Combine like terms: 0 + -46.25 = -46.25 14x + x2 = -46.25 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 = -46.25 + 49 Reorder the terms: 49 + 14x + x2 = -46.25 + 49 Combine like terms: -46.25 + 49 = 2.75 49 + 14x + x2 = 2.75 Factor a perfect square on the left side: (x + 7)(x + 7) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + 7) equal to 1.658312395 and -1.658312395.Subproblem 1
x + 7 = 1.658312395 Simplifying x + 7 = 1.658312395 Reorder the terms: 7 + x = 1.658312395 Solving 7 + x = 1.658312395 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 = 1.658312395 + -7 Combine like terms: 7 + -7 = 0 0 + x = 1.658312395 + -7 x = 1.658312395 + -7 Combine like terms: 1.658312395 + -7 = -5.341687605 x = -5.341687605 Simplifying x = -5.341687605Subproblem 2
x + 7 = -1.658312395 Simplifying x + 7 = -1.658312395 Reorder the terms: 7 + x = -1.658312395 Solving 7 + x = -1.658312395 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 = -1.658312395 + -7 Combine like terms: 7 + -7 = 0 0 + x = -1.658312395 + -7 x = -1.658312395 + -7 Combine like terms: -1.658312395 + -7 = -8.658312395 x = -8.658312395 Simplifying x = -8.658312395Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.341687605, -8.658312395}
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