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Simplifying 75 = 5x + x2 Solving 75 = 5x + x2 Solving for variable 'x'. Reorder the terms: 75 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 75 + -5x + -1x2 = 0 + x2 + -1x2 75 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 75 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -75 + 5x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 5x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 5x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 5x + x2 = 0 + 75 5x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 5x + x2 = 75 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 75 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 75 + 6.25 Combine like terms: 75 + 6.25 = 81.25 6.25 + 5x + x2 = 81.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + 2.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + 2.5 = 9.013878189 Simplifying x + 2.5 = 9.013878189 Reorder the terms: 2.5 + x = 9.013878189 Solving 2.5 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 9.013878189 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 9.013878189 + -2.5 x = 9.013878189 + -2.5 Combine like terms: 9.013878189 + -2.5 = 6.513878189 x = 6.513878189 Simplifying x = 6.513878189Subproblem 2
x + 2.5 = -9.013878189 Simplifying x + 2.5 = -9.013878189 Reorder the terms: 2.5 + x = -9.013878189 Solving 2.5 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -9.013878189 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -9.013878189 + -2.5 x = -9.013878189 + -2.5 Combine like terms: -9.013878189 + -2.5 = -11.513878189 x = -11.513878189 Simplifying x = -11.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.513878189, -11.513878189}
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