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Simplifying 36 = 7.5x + x * x Multiply x * x 36 = 7.5x + x2 Solving 36 = 7.5x + x2 Solving for variable 'x'. Reorder the terms: 36 + -7.5x + -1x2 = 7.5x + -7.5x + x2 + -1x2 Combine like terms: 7.5x + -7.5x = 0.0 36 + -7.5x + -1x2 = 0.0 + x2 + -1x2 36 + -7.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 36 + -7.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + 7.5x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 7.5x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 7.5x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 7.5x + x2 = 0 + 36 7.5x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 7.5x + x2 = 36 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 36 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 36 + 14.0625 Combine like terms: 36 + 14.0625 = 50.0625 14.0625 + 7.5x + x2 = 50.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 50.0625 Calculate the square root of the right side: 7.075485849 Break this problem into two subproblems by setting (x + 3.75) equal to 7.075485849 and -7.075485849.Subproblem 1
x + 3.75 = 7.075485849 Simplifying x + 3.75 = 7.075485849 Reorder the terms: 3.75 + x = 7.075485849 Solving 3.75 + x = 7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 7.075485849 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 7.075485849 + -3.75 x = 7.075485849 + -3.75 Combine like terms: 7.075485849 + -3.75 = 3.325485849 x = 3.325485849 Simplifying x = 3.325485849Subproblem 2
x + 3.75 = -7.075485849 Simplifying x + 3.75 = -7.075485849 Reorder the terms: 3.75 + x = -7.075485849 Solving 3.75 + x = -7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -7.075485849 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -7.075485849 + -3.75 x = -7.075485849 + -3.75 Combine like terms: -7.075485849 + -3.75 = -10.825485849 x = -10.825485849 Simplifying x = -10.825485849Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.325485849, -10.825485849}
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