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Simplifying x2 + -76x + 36 = 0 Reorder the terms: 36 + -76x + x2 = 0 Solving 36 + -76x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -76x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -76x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -76x + x2 = 0 + -36 -76x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -76x + x2 = -36 The x term is -76x. Take half its coefficient (-38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. -76x + 1444 + x2 = -36 + 1444 Reorder the terms: 1444 + -76x + x2 = -36 + 1444 Combine like terms: -36 + 1444 = 1408 1444 + -76x + x2 = 1408 Factor a perfect square on the left side: (x + -38)(x + -38) = 1408 Calculate the square root of the right side: 37.523326079 Break this problem into two subproblems by setting (x + -38) equal to 37.523326079 and -37.523326079.Subproblem 1
x + -38 = 37.523326079 Simplifying x + -38 = 37.523326079 Reorder the terms: -38 + x = 37.523326079 Solving -38 + x = 37.523326079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + x = 37.523326079 + 38 Combine like terms: -38 + 38 = 0 0 + x = 37.523326079 + 38 x = 37.523326079 + 38 Combine like terms: 37.523326079 + 38 = 75.523326079 x = 75.523326079 Simplifying x = 75.523326079Subproblem 2
x + -38 = -37.523326079 Simplifying x + -38 = -37.523326079 Reorder the terms: -38 + x = -37.523326079 Solving -38 + x = -37.523326079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + x = -37.523326079 + 38 Combine like terms: -38 + 38 = 0 0 + x = -37.523326079 + 38 x = -37.523326079 + 38 Combine like terms: -37.523326079 + 38 = 0.476673921 x = 0.476673921 Simplifying x = 0.476673921Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.523326079, 0.476673921}
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