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Simplifying 0 = 2.5x2 + -10.5x + 7 Reorder the terms: 0 = 7 + -10.5x + 2.5x2 Solving 0 = 7 + -10.5x + 2.5x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + 10.5x + -2.5x2 = 7 + -10.5x + 2.5x2 + -7 + 10.5x + -2.5x2 Reorder the terms: -7 + 10.5x + -2.5x2 = 7 + -7 + -10.5x + 10.5x + 2.5x2 + -2.5x2 Combine like terms: 7 + -7 = 0 -7 + 10.5x + -2.5x2 = 0 + -10.5x + 10.5x + 2.5x2 + -2.5x2 -7 + 10.5x + -2.5x2 = -10.5x + 10.5x + 2.5x2 + -2.5x2 Combine like terms: -10.5x + 10.5x = 0.0 -7 + 10.5x + -2.5x2 = 0.0 + 2.5x2 + -2.5x2 -7 + 10.5x + -2.5x2 = 2.5x2 + -2.5x2 Combine like terms: 2.5x2 + -2.5x2 = 0.0 -7 + 10.5x + -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'. 2.8 + -4.2x + x2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + -4.2x + -2.8 + x2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + -4.2x + x2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + -4.2x + x2 = 0 + -2.8 -4.2x + x2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 -4.2x + x2 = -2.8 The x term is -4.2x. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2x + 4.41 + x2 = -2.8 + 4.41 Reorder the terms: 4.41 + -4.2x + x2 = -2.8 + 4.41 Combine like terms: -2.8 + 4.41 = 1.61 4.41 + -4.2x + x2 = 1.61 Factor a perfect square on the left side: (x + -2.1)(x + -2.1) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (x + -2.1) equal to 1.268857754 and -1.268857754.Subproblem 1
x + -2.1 = 1.268857754 Simplifying x + -2.1 = 1.268857754 Reorder the terms: -2.1 + x = 1.268857754 Solving -2.1 + x = 1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = 1.268857754 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = 1.268857754 + 2.1 x = 1.268857754 + 2.1 Combine like terms: 1.268857754 + 2.1 = 3.368857754 x = 3.368857754 Simplifying x = 3.368857754Subproblem 2
x + -2.1 = -1.268857754 Simplifying x + -2.1 = -1.268857754 Reorder the terms: -2.1 + x = -1.268857754 Solving -2.1 + x = -1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = -1.268857754 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = -1.268857754 + 2.1 x = -1.268857754 + 2.1 Combine like terms: -1.268857754 + 2.1 = 0.831142246 x = 0.831142246 Simplifying x = 0.831142246Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.368857754, 0.831142246}
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