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Simplifying 25x + 275 = 2x2 + 6x + 7x + 3 Reorder the terms: 275 + 25x = 2x2 + 6x + 7x + 3 Reorder the terms: 275 + 25x = 3 + 6x + 7x + 2x2 Combine like terms: 6x + 7x = 13x 275 + 25x = 3 + 13x + 2x2 Solving 275 + 25x = 3 + 13x + 2x2 Solving for variable 'x'. Reorder the terms: 275 + -3 + 25x + -13x + -2x2 = 3 + 13x + 2x2 + -3 + -13x + -2x2 Combine like terms: 275 + -3 = 272 272 + 25x + -13x + -2x2 = 3 + 13x + 2x2 + -3 + -13x + -2x2 Combine like terms: 25x + -13x = 12x 272 + 12x + -2x2 = 3 + 13x + 2x2 + -3 + -13x + -2x2 Reorder the terms: 272 + 12x + -2x2 = 3 + -3 + 13x + -13x + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 272 + 12x + -2x2 = 0 + 13x + -13x + 2x2 + -2x2 272 + 12x + -2x2 = 13x + -13x + 2x2 + -2x2 Combine like terms: 13x + -13x = 0 272 + 12x + -2x2 = 0 + 2x2 + -2x2 272 + 12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 272 + 12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(136 + 6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(136 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 136 + 6x + -1x2 = 0 Solving 136 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -136 + -6x + x2 = 0 Move the constant term to the right: Add '136' to each side of the equation. -136 + -6x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + -6x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + -6x + x2 = 0 + 136 -6x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 -6x + x2 = 136 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 136 + 9 Reorder the terms: 9 + -6x + x2 = 136 + 9 Combine like terms: 136 + 9 = 145 9 + -6x + x2 = 145 Factor a perfect square on the left side: (x + -3)(x + -3) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + -3) equal to 12.041594579 and -12.041594579.Subproblem 1
x + -3 = 12.041594579 Simplifying x + -3 = 12.041594579 Reorder the terms: -3 + x = 12.041594579 Solving -3 + x = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 12.041594579 + 3 Combine like terms: -3 + 3 = 0 0 + x = 12.041594579 + 3 x = 12.041594579 + 3 Combine like terms: 12.041594579 + 3 = 15.041594579 x = 15.041594579 Simplifying x = 15.041594579Subproblem 2
x + -3 = -12.041594579 Simplifying x + -3 = -12.041594579 Reorder the terms: -3 + x = -12.041594579 Solving -3 + x = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -12.041594579 + 3 Combine like terms: -3 + 3 = 0 0 + x = -12.041594579 + 3 x = -12.041594579 + 3 Combine like terms: -12.041594579 + 3 = -9.041594579 x = -9.041594579 Simplifying x = -9.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.041594579, -9.041594579}Solution
x = {15.041594579, -9.041594579}
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