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Simplifying 2x2 + -3x + -76 = 0 Reorder the terms: -76 + -3x + 2x2 = 0 Solving -76 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -38 + -1.5x + x2 = 0 Move the constant term to the right: Add '38' to each side of the equation. -38 + -1.5x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -1.5x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -1.5x + x2 = 0 + 38 -1.5x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -1.5x + x2 = 38 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 38 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 38 + 0.5625 Combine like terms: 38 + 0.5625 = 38.5625 0.5625 + -1.5x + x2 = 38.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 38.5625 Calculate the square root of the right side: 6.209871174 Break this problem into two subproblems by setting (x + -0.75) equal to 6.209871174 and -6.209871174.Subproblem 1
x + -0.75 = 6.209871174 Simplifying x + -0.75 = 6.209871174 Reorder the terms: -0.75 + x = 6.209871174 Solving -0.75 + x = 6.209871174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 6.209871174 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 6.209871174 + 0.75 x = 6.209871174 + 0.75 Combine like terms: 6.209871174 + 0.75 = 6.959871174 x = 6.959871174 Simplifying x = 6.959871174Subproblem 2
x + -0.75 = -6.209871174 Simplifying x + -0.75 = -6.209871174 Reorder the terms: -0.75 + x = -6.209871174 Solving -0.75 + x = -6.209871174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -6.209871174 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -6.209871174 + 0.75 x = -6.209871174 + 0.75 Combine like terms: -6.209871174 + 0.75 = -5.459871174 x = -5.459871174 Simplifying x = -5.459871174Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.959871174, -5.459871174}
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