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Simplifying 25x2 + -95x + 61 = 0 Reorder the terms: 61 + -95x + 25x2 = 0 Solving 61 + -95x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 2.44 + -3.8x + x2 = 0 Move the constant term to the right: Add '-2.44' to each side of the equation. 2.44 + -3.8x + -2.44 + x2 = 0 + -2.44 Reorder the terms: 2.44 + -2.44 + -3.8x + x2 = 0 + -2.44 Combine like terms: 2.44 + -2.44 = 0.00 0.00 + -3.8x + x2 = 0 + -2.44 -3.8x + x2 = 0 + -2.44 Combine like terms: 0 + -2.44 = -2.44 -3.8x + x2 = -2.44 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = -2.44 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = -2.44 + 3.61 Combine like terms: -2.44 + 3.61 = 1.17 3.61 + -3.8x + x2 = 1.17 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = 1.17 Calculate the square root of the right side: 1.081665383 Break this problem into two subproblems by setting (x + -1.9) equal to 1.081665383 and -1.081665383.Subproblem 1
x + -1.9 = 1.081665383 Simplifying x + -1.9 = 1.081665383 Reorder the terms: -1.9 + x = 1.081665383 Solving -1.9 + x = 1.081665383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 1.081665383 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 1.081665383 + 1.9 x = 1.081665383 + 1.9 Combine like terms: 1.081665383 + 1.9 = 2.981665383 x = 2.981665383 Simplifying x = 2.981665383Subproblem 2
x + -1.9 = -1.081665383 Simplifying x + -1.9 = -1.081665383 Reorder the terms: -1.9 + x = -1.081665383 Solving -1.9 + x = -1.081665383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -1.081665383 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -1.081665383 + 1.9 x = -1.081665383 + 1.9 Combine like terms: -1.081665383 + 1.9 = 0.818334617 x = 0.818334617 Simplifying x = 0.818334617Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.981665383, 0.818334617}
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