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Simplifying 2x2 + 3x + -6.875 = 0 Reorder the terms: -6.875 + 3x + 2x2 = 0 Solving -6.875 + 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'. -3.4375 + 1.5x + x2 = 0 Move the constant term to the right: Add '3.4375' to each side of the equation. -3.4375 + 1.5x + 3.4375 + x2 = 0 + 3.4375 Reorder the terms: -3.4375 + 3.4375 + 1.5x + x2 = 0 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + 1.5x + x2 = 0 + 3.4375 1.5x + x2 = 0 + 3.4375 Combine like terms: 0 + 3.4375 = 3.4375 1.5x + x2 = 3.4375 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 = 3.4375 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 3.4375 + 0.5625 Combine like terms: 3.4375 + 0.5625 = 4 0.5625 + 1.5x + x2 = 4 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + 0.75) equal to 2 and -2.Subproblem 1
x + 0.75 = 2 Simplifying x + 0.75 = 2 Reorder the terms: 0.75 + x = 2 Solving 0.75 + x = 2 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 = 2 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2 + -0.75 x = 2 + -0.75 Combine like terms: 2 + -0.75 = 1.25 x = 1.25 Simplifying x = 1.25Subproblem 2
x + 0.75 = -2 Simplifying x + 0.75 = -2 Reorder the terms: 0.75 + x = -2 Solving 0.75 + x = -2 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 = -2 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2 + -0.75 x = -2 + -0.75 Combine like terms: -2 + -0.75 = -2.75 x = -2.75 Simplifying x = -2.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.25, -2.75}
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