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Simplifying 4x2 + 20x + -95 = 0 Reorder the terms: -95 + 20x + 4x2 = 0 Solving -95 + 20x + 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'. -23.75 + 5x + x2 = 0 Move the constant term to the right: Add '23.75' to each side of the equation. -23.75 + 5x + 23.75 + x2 = 0 + 23.75 Reorder the terms: -23.75 + 23.75 + 5x + x2 = 0 + 23.75 Combine like terms: -23.75 + 23.75 = 0.00 0.00 + 5x + x2 = 0 + 23.75 5x + x2 = 0 + 23.75 Combine like terms: 0 + 23.75 = 23.75 5x + x2 = 23.75 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 23.75 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 23.75 + 6.25 Combine like terms: 23.75 + 6.25 = 30 6.25 + 5x + x2 = 30 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 2.5) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 2.5 = 5.477225575 Simplifying x + 2.5 = 5.477225575 Reorder the terms: 2.5 + x = 5.477225575 Solving 2.5 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.477225575 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.477225575 + -2.5 x = 5.477225575 + -2.5 Combine like terms: 5.477225575 + -2.5 = 2.977225575 x = 2.977225575 Simplifying x = 2.977225575Subproblem 2
x + 2.5 = -5.477225575 Simplifying x + 2.5 = -5.477225575 Reorder the terms: 2.5 + x = -5.477225575 Solving 2.5 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.477225575 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.477225575 + -2.5 x = -5.477225575 + -2.5 Combine like terms: -5.477225575 + -2.5 = -7.977225575 x = -7.977225575 Simplifying x = -7.977225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.977225575, -7.977225575}
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