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Simplifying 13.125 + 2.5x + 2.5x2 = 100 Solving 13.125 + 2.5x + 2.5x2 = 100 Solving for variable 'x'. Reorder the terms: 13.125 + -100 + 2.5x + 2.5x2 = 100 + -100 Combine like terms: 13.125 + -100 = -86.875 -86.875 + 2.5x + 2.5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -86.875 + 2.5x + 2.5x2 = 0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -34.75 + x + x2 = 0 Move the constant term to the right: Add '34.75' to each side of the equation. -34.75 + x + 34.75 + x2 = 0 + 34.75 Reorder the terms: -34.75 + 34.75 + x + x2 = 0 + 34.75 Combine like terms: -34.75 + 34.75 = 0.00 0.00 + x + x2 = 0 + 34.75 x + x2 = 0 + 34.75 Combine like terms: 0 + 34.75 = 34.75 x + x2 = 34.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 34.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 34.75 + 0.25 Combine like terms: 34.75 + 0.25 = 35 1.25 + x2 = 35 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + 0.5) equal to 5.916079783 and -5.916079783.Subproblem 1
x + 0.5 = 5.916079783 Simplifying x + 0.5 = 5.916079783 Reorder the terms: 0.5 + x = 5.916079783 Solving 0.5 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.916079783 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.916079783 + -0.5 x = 5.916079783 + -0.5 Combine like terms: 5.916079783 + -0.5 = 5.416079783 x = 5.416079783 Simplifying x = 5.416079783Subproblem 2
x + 0.5 = -5.916079783 Simplifying x + 0.5 = -5.916079783 Reorder the terms: 0.5 + x = -5.916079783 Solving 0.5 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.916079783 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.916079783 + -0.5 x = -5.916079783 + -0.5 Combine like terms: -5.916079783 + -0.5 = -6.416079783 x = -6.416079783 Simplifying x = -6.416079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.416079783, -6.416079783}
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