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Simplifying -5x2 + 40x + -59 = -3x2 + 26 Reorder the terms: -59 + 40x + -5x2 = -3x2 + 26 Reorder the terms: -59 + 40x + -5x2 = 26 + -3x2 Solving -59 + 40x + -5x2 = 26 + -3x2 Solving for variable 'x'. Reorder the terms: -59 + -26 + 40x + -5x2 + 3x2 = 26 + -3x2 + -26 + 3x2 Combine like terms: -59 + -26 = -85 -85 + 40x + -5x2 + 3x2 = 26 + -3x2 + -26 + 3x2 Combine like terms: -5x2 + 3x2 = -2x2 -85 + 40x + -2x2 = 26 + -3x2 + -26 + 3x2 Reorder the terms: -85 + 40x + -2x2 = 26 + -26 + -3x2 + 3x2 Combine like terms: 26 + -26 = 0 -85 + 40x + -2x2 = 0 + -3x2 + 3x2 -85 + 40x + -2x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -85 + 40x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 42.5 + -20x + x2 = 0 Move the constant term to the right: Add '-42.5' to each side of the equation. 42.5 + -20x + -42.5 + x2 = 0 + -42.5 Reorder the terms: 42.5 + -42.5 + -20x + x2 = 0 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + -20x + x2 = 0 + -42.5 -20x + x2 = 0 + -42.5 Combine like terms: 0 + -42.5 = -42.5 -20x + x2 = -42.5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -42.5 + 100 Reorder the terms: 100 + -20x + x2 = -42.5 + 100 Combine like terms: -42.5 + 100 = 57.5 100 + -20x + x2 = 57.5 Factor a perfect square on the left side: (x + -10)(x + -10) = 57.5 Calculate the square root of the right side: 7.582875444 Break this problem into two subproblems by setting (x + -10) equal to 7.582875444 and -7.582875444.Subproblem 1
x + -10 = 7.582875444 Simplifying x + -10 = 7.582875444 Reorder the terms: -10 + x = 7.582875444 Solving -10 + x = 7.582875444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 7.582875444 + 10 Combine like terms: -10 + 10 = 0 0 + x = 7.582875444 + 10 x = 7.582875444 + 10 Combine like terms: 7.582875444 + 10 = 17.582875444 x = 17.582875444 Simplifying x = 17.582875444Subproblem 2
x + -10 = -7.582875444 Simplifying x + -10 = -7.582875444 Reorder the terms: -10 + x = -7.582875444 Solving -10 + x = -7.582875444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -7.582875444 + 10 Combine like terms: -10 + 10 = 0 0 + x = -7.582875444 + 10 x = -7.582875444 + 10 Combine like terms: -7.582875444 + 10 = 2.417124556 x = 2.417124556 Simplifying x = 2.417124556Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.582875444, 2.417124556}
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