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Simplifying 13x2 + -570x + -1872 = 0 Reorder the terms: -1872 + -570x + 13x2 = 0 Solving -1872 + -570x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -144 + -43.84615385x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + -43.84615385x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -43.84615385x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -43.84615385x + x2 = 0 + 144 -43.84615385x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -43.84615385x + x2 = 144 The x term is -43.84615385x. Take half its coefficient (-21.92307693). Square it (480.6213021) and add it to both sides. Add '480.6213021' to each side of the equation. -43.84615385x + 480.6213021 + x2 = 144 + 480.6213021 Reorder the terms: 480.6213021 + -43.84615385x + x2 = 144 + 480.6213021 Combine like terms: 144 + 480.6213021 = 624.6213021 480.6213021 + -43.84615385x + x2 = 624.6213021 Factor a perfect square on the left side: (x + -21.92307693)(x + -21.92307693) = 624.6213021 Calculate the square root of the right side: 24.992424894 Break this problem into two subproblems by setting (x + -21.92307693) equal to 24.992424894 and -24.992424894.Subproblem 1
x + -21.92307693 = 24.992424894 Simplifying x + -21.92307693 = 24.992424894 Reorder the terms: -21.92307693 + x = 24.992424894 Solving -21.92307693 + x = 24.992424894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.92307693' to each side of the equation. -21.92307693 + 21.92307693 + x = 24.992424894 + 21.92307693 Combine like terms: -21.92307693 + 21.92307693 = 0.00000000 0.00000000 + x = 24.992424894 + 21.92307693 x = 24.992424894 + 21.92307693 Combine like terms: 24.992424894 + 21.92307693 = 46.915501824 x = 46.915501824 Simplifying x = 46.915501824Subproblem 2
x + -21.92307693 = -24.992424894 Simplifying x + -21.92307693 = -24.992424894 Reorder the terms: -21.92307693 + x = -24.992424894 Solving -21.92307693 + x = -24.992424894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.92307693' to each side of the equation. -21.92307693 + 21.92307693 + x = -24.992424894 + 21.92307693 Combine like terms: -21.92307693 + 21.92307693 = 0.00000000 0.00000000 + x = -24.992424894 + 21.92307693 x = -24.992424894 + 21.92307693 Combine like terms: -24.992424894 + 21.92307693 = -3.069347964 x = -3.069347964 Simplifying x = -3.069347964Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.915501824, -3.069347964}
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