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Simplifying 0.9x(x + -350) = 20 Reorder the terms: 0.9x(-350 + x) = 20 (-350 * 0.9x + x * 0.9x) = 20 (-315x + 0.9x2) = 20 Solving -315x + 0.9x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -315x + 0.9x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -315x + 0.9x2 = 0 Begin completing the square. Divide all terms by 0.9 the coefficient of the squared term: Divide each side by '0.9'. -22.22222222 + -350x + x2 = 0 Move the constant term to the right: Add '22.22222222' to each side of the equation. -22.22222222 + -350x + 22.22222222 + x2 = 0 + 22.22222222 Reorder the terms: -22.22222222 + 22.22222222 + -350x + x2 = 0 + 22.22222222 Combine like terms: -22.22222222 + 22.22222222 = 0.00000000 0.00000000 + -350x + x2 = 0 + 22.22222222 -350x + x2 = 0 + 22.22222222 Combine like terms: 0 + 22.22222222 = 22.22222222 -350x + x2 = 22.22222222 The x term is -350x. Take half its coefficient (-175). Square it (30625) and add it to both sides. Add '30625' to each side of the equation. -350x + 30625 + x2 = 22.22222222 + 30625 Reorder the terms: 30625 + -350x + x2 = 22.22222222 + 30625 Combine like terms: 22.22222222 + 30625 = 30647.22222222 30625 + -350x + x2 = 30647.22222222 Factor a perfect square on the left side: (x + -175)(x + -175) = 30647.22222222 Calculate the square root of the right side: 175.06348055 Break this problem into two subproblems by setting (x + -175) equal to 175.06348055 and -175.06348055.Subproblem 1
x + -175 = 175.06348055 Simplifying x + -175 = 175.06348055 Reorder the terms: -175 + x = 175.06348055 Solving -175 + x = 175.06348055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '175' to each side of the equation. -175 + 175 + x = 175.06348055 + 175 Combine like terms: -175 + 175 = 0 0 + x = 175.06348055 + 175 x = 175.06348055 + 175 Combine like terms: 175.06348055 + 175 = 350.06348055 x = 350.06348055 Simplifying x = 350.06348055Subproblem 2
x + -175 = -175.06348055 Simplifying x + -175 = -175.06348055 Reorder the terms: -175 + x = -175.06348055 Solving -175 + x = -175.06348055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '175' to each side of the equation. -175 + 175 + x = -175.06348055 + 175 Combine like terms: -175 + 175 = 0 0 + x = -175.06348055 + 175 x = -175.06348055 + 175 Combine like terms: -175.06348055 + 175 = -0.06348055 x = -0.06348055 Simplifying x = -0.06348055Solution
The solution to the problem is based on the solutions from the subproblems. x = {350.06348055, -0.06348055}
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