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Simplifying x2 + x2 + 10x + 25 = 4x2 + -50x + 100 Reorder the terms: 25 + 10x + x2 + x2 = 4x2 + -50x + 100 Combine like terms: x2 + x2 = 2x2 25 + 10x + 2x2 = 4x2 + -50x + 100 Reorder the terms: 25 + 10x + 2x2 = 100 + -50x + 4x2 Solving 25 + 10x + 2x2 = 100 + -50x + 4x2 Solving for variable 'x'. Reorder the terms: 25 + -100 + 10x + 50x + 2x2 + -4x2 = 100 + -50x + 4x2 + -100 + 50x + -4x2 Combine like terms: 25 + -100 = -75 -75 + 10x + 50x + 2x2 + -4x2 = 100 + -50x + 4x2 + -100 + 50x + -4x2 Combine like terms: 10x + 50x = 60x -75 + 60x + 2x2 + -4x2 = 100 + -50x + 4x2 + -100 + 50x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 -75 + 60x + -2x2 = 100 + -50x + 4x2 + -100 + 50x + -4x2 Reorder the terms: -75 + 60x + -2x2 = 100 + -100 + -50x + 50x + 4x2 + -4x2 Combine like terms: 100 + -100 = 0 -75 + 60x + -2x2 = 0 + -50x + 50x + 4x2 + -4x2 -75 + 60x + -2x2 = -50x + 50x + 4x2 + -4x2 Combine like terms: -50x + 50x = 0 -75 + 60x + -2x2 = 0 + 4x2 + -4x2 -75 + 60x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -75 + 60x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 37.5 + -30x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -30x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -30x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -30x + x2 = 0 + -37.5 -30x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -30x + x2 = -37.5 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -37.5 + 225 Reorder the terms: 225 + -30x + x2 = -37.5 + 225 Combine like terms: -37.5 + 225 = 187.5 225 + -30x + x2 = 187.5 Factor a perfect square on the left side: (x + -15)(x + -15) = 187.5 Calculate the square root of the right side: 13.693063938 Break this problem into two subproblems by setting (x + -15) equal to 13.693063938 and -13.693063938.Subproblem 1
x + -15 = 13.693063938 Simplifying x + -15 = 13.693063938 Reorder the terms: -15 + x = 13.693063938 Solving -15 + x = 13.693063938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 13.693063938 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.693063938 + 15 x = 13.693063938 + 15 Combine like terms: 13.693063938 + 15 = 28.693063938 x = 28.693063938 Simplifying x = 28.693063938Subproblem 2
x + -15 = -13.693063938 Simplifying x + -15 = -13.693063938 Reorder the terms: -15 + x = -13.693063938 Solving -15 + x = -13.693063938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -13.693063938 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.693063938 + 15 x = -13.693063938 + 15 Combine like terms: -13.693063938 + 15 = 1.306936062 x = 1.306936062 Simplifying x = 1.306936062Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.693063938, 1.306936062}
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