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Simplifying x2 + 3 = -74x Reorder the terms: 3 + x2 = -74x Solving 3 + x2 = -74x Solving for variable 'x'. Reorder the terms: 3 + 74x + x2 = -74x + 74x Combine like terms: -74x + 74x = 0 3 + 74x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 74x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 74x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 74x + x2 = 0 + -3 74x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 74x + x2 = -3 The x term is 74x. Take half its coefficient (37). Square it (1369) and add it to both sides. Add '1369' to each side of the equation. 74x + 1369 + x2 = -3 + 1369 Reorder the terms: 1369 + 74x + x2 = -3 + 1369 Combine like terms: -3 + 1369 = 1366 1369 + 74x + x2 = 1366 Factor a perfect square on the left side: (x + 37)(x + 37) = 1366 Calculate the square root of the right side: 36.959437225 Break this problem into two subproblems by setting (x + 37) equal to 36.959437225 and -36.959437225.Subproblem 1
x + 37 = 36.959437225 Simplifying x + 37 = 36.959437225 Reorder the terms: 37 + x = 36.959437225 Solving 37 + x = 36.959437225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + x = 36.959437225 + -37 Combine like terms: 37 + -37 = 0 0 + x = 36.959437225 + -37 x = 36.959437225 + -37 Combine like terms: 36.959437225 + -37 = -0.040562775 x = -0.040562775 Simplifying x = -0.040562775Subproblem 2
x + 37 = -36.959437225 Simplifying x + 37 = -36.959437225 Reorder the terms: 37 + x = -36.959437225 Solving 37 + x = -36.959437225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + x = -36.959437225 + -37 Combine like terms: 37 + -37 = 0 0 + x = -36.959437225 + -37 x = -36.959437225 + -37 Combine like terms: -36.959437225 + -37 = -73.959437225 x = -73.959437225 Simplifying x = -73.959437225Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.040562775, -73.959437225}
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