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Simplifying x = 2x + x2 + 3(4x) + 17 Remove parenthesis around (4x) x = 2x + x2 + 3 * 4x + 17 Multiply 3 * 4 x = 2x + x2 + 12x + 17 Reorder the terms: x = 17 + 2x + 12x + x2 Combine like terms: 2x + 12x = 14x x = 17 + 14x + x2 Solving x = 17 + 14x + x2 Solving for variable 'x'. Reorder the terms: -17 + x + -14x + -1x2 = 17 + 14x + x2 + -17 + -14x + -1x2 Combine like terms: x + -14x = -13x -17 + -13x + -1x2 = 17 + 14x + x2 + -17 + -14x + -1x2 Reorder the terms: -17 + -13x + -1x2 = 17 + -17 + 14x + -14x + x2 + -1x2 Combine like terms: 17 + -17 = 0 -17 + -13x + -1x2 = 0 + 14x + -14x + x2 + -1x2 -17 + -13x + -1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 -17 + -13x + -1x2 = 0 + x2 + -1x2 -17 + -13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -17 + -13x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 13x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 13x + x2)' equal to zero and attempt to solve: Simplifying 17 + 13x + x2 = 0 Solving 17 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 13x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 13x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 13x + x2 = 0 + -17 13x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 13x + x2 = -17 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -17 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -17 + 42.25 Combine like terms: -17 + 42.25 = 25.25 42.25 + 13x + x2 = 25.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + 6.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + 6.5 = 5.024937811 Simplifying x + 6.5 = 5.024937811 Reorder the terms: 6.5 + x = 5.024937811 Solving 6.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 5.024937811 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 5.024937811 + -6.5 x = 5.024937811 + -6.5 Combine like terms: 5.024937811 + -6.5 = -1.475062189 x = -1.475062189 Simplifying x = -1.475062189Subproblem 2
x + 6.5 = -5.024937811 Simplifying x + 6.5 = -5.024937811 Reorder the terms: 6.5 + x = -5.024937811 Solving 6.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -5.024937811 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -5.024937811 + -6.5 x = -5.024937811 + -6.5 Combine like terms: -5.024937811 + -6.5 = -11.524937811 x = -11.524937811 Simplifying x = -11.524937811Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.475062189, -11.524937811}Solution
x = {-1.475062189, -11.524937811}
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