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Simplifying 2x2 + -7x + -74 = 0 Reorder the terms: -74 + -7x + 2x2 = 0 Solving -74 + -7x + 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'. -37 + -3.5x + x2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + -3.5x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + -3.5x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -3.5x + x2 = 0 + 37 -3.5x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 -3.5x + x2 = 37 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 37 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 37 + 3.0625 Combine like terms: 37 + 3.0625 = 40.0625 3.0625 + -3.5x + x2 = 40.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 40.0625 Calculate the square root of the right side: 6.329494451 Break this problem into two subproblems by setting (x + -1.75) equal to 6.329494451 and -6.329494451.Subproblem 1
x + -1.75 = 6.329494451 Simplifying x + -1.75 = 6.329494451 Reorder the terms: -1.75 + x = 6.329494451 Solving -1.75 + x = 6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 6.329494451 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 6.329494451 + 1.75 x = 6.329494451 + 1.75 Combine like terms: 6.329494451 + 1.75 = 8.079494451 x = 8.079494451 Simplifying x = 8.079494451Subproblem 2
x + -1.75 = -6.329494451 Simplifying x + -1.75 = -6.329494451 Reorder the terms: -1.75 + x = -6.329494451 Solving -1.75 + x = -6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -6.329494451 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -6.329494451 + 1.75 x = -6.329494451 + 1.75 Combine like terms: -6.329494451 + 1.75 = -4.579494451 x = -4.579494451 Simplifying x = -4.579494451Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.079494451, -4.579494451}
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