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Simplifying -0.02x2 + 1.21x + 2.5 = 0 Reorder the terms: 2.5 + 1.21x + -0.02x2 = 0 Solving 2.5 + 1.21x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. -125 + -60.5x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + -60.5x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -60.5x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -60.5x + x2 = 0 + 125 -60.5x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -60.5x + x2 = 125 The x term is -60.5x. Take half its coefficient (-30.25). Square it (915.0625) and add it to both sides. Add '915.0625' to each side of the equation. -60.5x + 915.0625 + x2 = 125 + 915.0625 Reorder the terms: 915.0625 + -60.5x + x2 = 125 + 915.0625 Combine like terms: 125 + 915.0625 = 1040.0625 915.0625 + -60.5x + x2 = 1040.0625 Factor a perfect square on the left side: (x + -30.25)(x + -30.25) = 1040.0625 Calculate the square root of the right side: 32.25 Break this problem into two subproblems by setting (x + -30.25) equal to 32.25 and -32.25.Subproblem 1
x + -30.25 = 32.25 Simplifying x + -30.25 = 32.25 Reorder the terms: -30.25 + x = 32.25 Solving -30.25 + x = 32.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.25' to each side of the equation. -30.25 + 30.25 + x = 32.25 + 30.25 Combine like terms: -30.25 + 30.25 = 0.00 0.00 + x = 32.25 + 30.25 x = 32.25 + 30.25 Combine like terms: 32.25 + 30.25 = 62.5 x = 62.5 Simplifying x = 62.5Subproblem 2
x + -30.25 = -32.25 Simplifying x + -30.25 = -32.25 Reorder the terms: -30.25 + x = -32.25 Solving -30.25 + x = -32.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.25' to each side of the equation. -30.25 + 30.25 + x = -32.25 + 30.25 Combine like terms: -30.25 + 30.25 = 0.00 0.00 + x = -32.25 + 30.25 x = -32.25 + 30.25 Combine like terms: -32.25 + 30.25 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.5, -2}
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