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Simplifying x2 + 37.5x + 400 = 1400x Reorder the terms: 400 + 37.5x + x2 = 1400x Solving 400 + 37.5x + x2 = 1400x Solving for variable 'x'. Reorder the terms: 400 + 37.5x + -1400x + x2 = 1400x + -1400x Combine like terms: 37.5x + -1400x = -1362.5x 400 + -1362.5x + x2 = 1400x + -1400x Combine like terms: 1400x + -1400x = 0 400 + -1362.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-400' to each side of the equation. 400 + -1362.5x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -1362.5x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -1362.5x + x2 = 0 + -400 -1362.5x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -1362.5x + x2 = -400 The x term is -1362.5x. Take half its coefficient (-681.25). Square it (464101.5625) and add it to both sides. Add '464101.5625' to each side of the equation. -1362.5x + 464101.5625 + x2 = -400 + 464101.5625 Reorder the terms: 464101.5625 + -1362.5x + x2 = -400 + 464101.5625 Combine like terms: -400 + 464101.5625 = 463701.5625 464101.5625 + -1362.5x + x2 = 463701.5625 Factor a perfect square on the left side: (x + -681.25)(x + -681.25) = 463701.5625 Calculate the square root of the right side: 680.956358734 Break this problem into two subproblems by setting (x + -681.25) equal to 680.956358734 and -680.956358734.Subproblem 1
x + -681.25 = 680.956358734 Simplifying x + -681.25 = 680.956358734 Reorder the terms: -681.25 + x = 680.956358734 Solving -681.25 + x = 680.956358734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '681.25' to each side of the equation. -681.25 + 681.25 + x = 680.956358734 + 681.25 Combine like terms: -681.25 + 681.25 = 0.00 0.00 + x = 680.956358734 + 681.25 x = 680.956358734 + 681.25 Combine like terms: 680.956358734 + 681.25 = 1362.206358734 x = 1362.206358734 Simplifying x = 1362.206358734Subproblem 2
x + -681.25 = -680.956358734 Simplifying x + -681.25 = -680.956358734 Reorder the terms: -681.25 + x = -680.956358734 Solving -681.25 + x = -680.956358734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '681.25' to each side of the equation. -681.25 + 681.25 + x = -680.956358734 + 681.25 Combine like terms: -681.25 + 681.25 = 0.00 0.00 + x = -680.956358734 + 681.25 x = -680.956358734 + 681.25 Combine like terms: -680.956358734 + 681.25 = 0.293641266 x = 0.293641266 Simplifying x = 0.293641266Solution
The solution to the problem is based on the solutions from the subproblems. x = {1362.206358734, 0.293641266}
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