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Simplifying 2x2 + -300x + 5625 = 0 Reorder the terms: 5625 + -300x + 2x2 = 0 Solving 5625 + -300x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2812.5 + -150x + x2 = 0 Move the constant term to the right: Add '-2812.5' to each side of the equation. 2812.5 + -150x + -2812.5 + x2 = 0 + -2812.5 Reorder the terms: 2812.5 + -2812.5 + -150x + x2 = 0 + -2812.5 Combine like terms: 2812.5 + -2812.5 = 0.0 0.0 + -150x + x2 = 0 + -2812.5 -150x + x2 = 0 + -2812.5 Combine like terms: 0 + -2812.5 = -2812.5 -150x + x2 = -2812.5 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = -2812.5 + 5625 Reorder the terms: 5625 + -150x + x2 = -2812.5 + 5625 Combine like terms: -2812.5 + 5625 = 2812.5 5625 + -150x + x2 = 2812.5 Factor a perfect square on the left side: (x + -75)(x + -75) = 2812.5 Calculate the square root of the right side: 53.033008589 Break this problem into two subproblems by setting (x + -75) equal to 53.033008589 and -53.033008589.Subproblem 1
x + -75 = 53.033008589 Simplifying x + -75 = 53.033008589 Reorder the terms: -75 + x = 53.033008589 Solving -75 + x = 53.033008589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 53.033008589 + 75 Combine like terms: -75 + 75 = 0 0 + x = 53.033008589 + 75 x = 53.033008589 + 75 Combine like terms: 53.033008589 + 75 = 128.033008589 x = 128.033008589 Simplifying x = 128.033008589Subproblem 2
x + -75 = -53.033008589 Simplifying x + -75 = -53.033008589 Reorder the terms: -75 + x = -53.033008589 Solving -75 + x = -53.033008589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -53.033008589 + 75 Combine like terms: -75 + 75 = 0 0 + x = -53.033008589 + 75 x = -53.033008589 + 75 Combine like terms: -53.033008589 + 75 = 21.966991411 x = 21.966991411 Simplifying x = 21.966991411Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.033008589, 21.966991411}
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