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Simplifying -2.5x2 + 5.75x = 2.1 Reorder the terms: 5.75x + -2.5x2 = 2.1 Solving 5.75x + -2.5x2 = 2.1 Solving for variable 'x'. Reorder the terms: -2.1 + 5.75x + -2.5x2 = 2.1 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 -2.1 + 5.75x + -2.5x2 = 0.0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. 0.84 + -2.3x + x2 = 0 Move the constant term to the right: Add '-0.84' to each side of the equation. 0.84 + -2.3x + -0.84 + x2 = 0 + -0.84 Reorder the terms: 0.84 + -0.84 + -2.3x + x2 = 0 + -0.84 Combine like terms: 0.84 + -0.84 = 0.00 0.00 + -2.3x + x2 = 0 + -0.84 -2.3x + x2 = 0 + -0.84 Combine like terms: 0 + -0.84 = -0.84 -2.3x + x2 = -0.84 The x term is -2.3x. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3x + 1.3225 + x2 = -0.84 + 1.3225 Reorder the terms: 1.3225 + -2.3x + x2 = -0.84 + 1.3225 Combine like terms: -0.84 + 1.3225 = 0.4825 1.3225 + -2.3x + x2 = 0.4825 Factor a perfect square on the left side: (x + -1.15)(x + -1.15) = 0.4825 Calculate the square root of the right side: 0.694622199 Break this problem into two subproblems by setting (x + -1.15) equal to 0.694622199 and -0.694622199.Subproblem 1
x + -1.15 = 0.694622199 Simplifying x + -1.15 = 0.694622199 Reorder the terms: -1.15 + x = 0.694622199 Solving -1.15 + x = 0.694622199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = 0.694622199 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = 0.694622199 + 1.15 x = 0.694622199 + 1.15 Combine like terms: 0.694622199 + 1.15 = 1.844622199 x = 1.844622199 Simplifying x = 1.844622199Subproblem 2
x + -1.15 = -0.694622199 Simplifying x + -1.15 = -0.694622199 Reorder the terms: -1.15 + x = -0.694622199 Solving -1.15 + x = -0.694622199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = -0.694622199 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = -0.694622199 + 1.15 x = -0.694622199 + 1.15 Combine like terms: -0.694622199 + 1.15 = 0.455377801 x = 0.455377801 Simplifying x = 0.455377801Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.844622199, 0.455377801}
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