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Simplifying 2x2 + 3.5x + -67.5 = 0 Reorder the terms: -67.5 + 3.5x + 2x2 = 0 Solving -67.5 + 3.5x + 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'. -33.75 + 1.75x + x2 = 0 Move the constant term to the right: Add '33.75' to each side of the equation. -33.75 + 1.75x + 33.75 + x2 = 0 + 33.75 Reorder the terms: -33.75 + 33.75 + 1.75x + x2 = 0 + 33.75 Combine like terms: -33.75 + 33.75 = 0.00 0.00 + 1.75x + x2 = 0 + 33.75 1.75x + x2 = 0 + 33.75 Combine like terms: 0 + 33.75 = 33.75 1.75x + x2 = 33.75 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 33.75 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 33.75 + 0.765625 Combine like terms: 33.75 + 0.765625 = 34.515625 0.765625 + 1.75x + x2 = 34.515625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 34.515625 Calculate the square root of the right side: 5.875 Break this problem into two subproblems by setting (x + 0.875) equal to 5.875 and -5.875.Subproblem 1
x + 0.875 = 5.875 Simplifying x + 0.875 = 5.875 Reorder the terms: 0.875 + x = 5.875 Solving 0.875 + x = 5.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 5.875 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 5.875 + -0.875 x = 5.875 + -0.875 Combine like terms: 5.875 + -0.875 = 5 x = 5 Simplifying x = 5Subproblem 2
x + 0.875 = -5.875 Simplifying x + 0.875 = -5.875 Reorder the terms: 0.875 + x = -5.875 Solving 0.875 + x = -5.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -5.875 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -5.875 + -0.875 x = -5.875 + -0.875 Combine like terms: -5.875 + -0.875 = -6.75 x = -6.75 Simplifying x = -6.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -6.75}
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