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Simplifying x2 + -300x + 5675 = 0 Reorder the terms: 5675 + -300x + x2 = 0 Solving 5675 + -300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5675' to each side of the equation. 5675 + -300x + -5675 + x2 = 0 + -5675 Reorder the terms: 5675 + -5675 + -300x + x2 = 0 + -5675 Combine like terms: 5675 + -5675 = 0 0 + -300x + x2 = 0 + -5675 -300x + x2 = 0 + -5675 Combine like terms: 0 + -5675 = -5675 -300x + x2 = -5675 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = -5675 + 22500 Reorder the terms: 22500 + -300x + x2 = -5675 + 22500 Combine like terms: -5675 + 22500 = 16825 22500 + -300x + x2 = 16825 Factor a perfect square on the left side: (x + -150)(x + -150) = 16825 Calculate the square root of the right side: 129.711217711 Break this problem into two subproblems by setting (x + -150) equal to 129.711217711 and -129.711217711.Subproblem 1
x + -150 = 129.711217711 Simplifying x + -150 = 129.711217711 Reorder the terms: -150 + x = 129.711217711 Solving -150 + x = 129.711217711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 129.711217711 + 150 Combine like terms: -150 + 150 = 0 0 + x = 129.711217711 + 150 x = 129.711217711 + 150 Combine like terms: 129.711217711 + 150 = 279.711217711 x = 279.711217711 Simplifying x = 279.711217711Subproblem 2
x + -150 = -129.711217711 Simplifying x + -150 = -129.711217711 Reorder the terms: -150 + x = -129.711217711 Solving -150 + x = -129.711217711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -129.711217711 + 150 Combine like terms: -150 + 150 = 0 0 + x = -129.711217711 + 150 x = -129.711217711 + 150 Combine like terms: -129.711217711 + 150 = 20.288782289 x = 20.288782289 Simplifying x = 20.288782289Solution
The solution to the problem is based on the solutions from the subproblems. x = {279.711217711, 20.288782289}
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