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Simplifying x(2x + 5) + 6x + -17(3x + 2) = 12x + -10 Reorder the terms: x(5 + 2x) + 6x + -17(3x + 2) = 12x + -10 (5 * x + 2x * x) + 6x + -17(3x + 2) = 12x + -10 (5x + 2x2) + 6x + -17(3x + 2) = 12x + -10 Reorder the terms: 5x + 2x2 + 6x + -17(2 + 3x) = 12x + -10 5x + 2x2 + 6x + (2 * -17 + 3x * -17) = 12x + -10 5x + 2x2 + 6x + (-34 + -51x) = 12x + -10 Reorder the terms: -34 + 5x + 6x + -51x + 2x2 = 12x + -10 Combine like terms: 5x + 6x = 11x -34 + 11x + -51x + 2x2 = 12x + -10 Combine like terms: 11x + -51x = -40x -34 + -40x + 2x2 = 12x + -10 Reorder the terms: -34 + -40x + 2x2 = -10 + 12x Solving -34 + -40x + 2x2 = -10 + 12x Solving for variable 'x'. Reorder the terms: -34 + 10 + -40x + -12x + 2x2 = -10 + 12x + 10 + -12x Combine like terms: -34 + 10 = -24 -24 + -40x + -12x + 2x2 = -10 + 12x + 10 + -12x Combine like terms: -40x + -12x = -52x -24 + -52x + 2x2 = -10 + 12x + 10 + -12x Reorder the terms: -24 + -52x + 2x2 = -10 + 10 + 12x + -12x Combine like terms: -10 + 10 = 0 -24 + -52x + 2x2 = 0 + 12x + -12x -24 + -52x + 2x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -24 + -52x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -26x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -26x + x2)' equal to zero and attempt to solve: Simplifying -12 + -26x + x2 = 0 Solving -12 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -26x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -26x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -26x + x2 = 0 + 12 -26x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -26x + x2 = 12 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 12 + 169 Reorder the terms: 169 + -26x + x2 = 12 + 169 Combine like terms: 12 + 169 = 181 169 + -26x + x2 = 181 Factor a perfect square on the left side: (x + -13)(x + -13) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (x + -13) equal to 13.453624047 and -13.453624047.Subproblem 1
x + -13 = 13.453624047 Simplifying x + -13 = 13.453624047 Reorder the terms: -13 + x = 13.453624047 Solving -13 + x = 13.453624047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 13.453624047 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.453624047 + 13 x = 13.453624047 + 13 Combine like terms: 13.453624047 + 13 = 26.453624047 x = 26.453624047 Simplifying x = 26.453624047Subproblem 2
x + -13 = -13.453624047 Simplifying x + -13 = -13.453624047 Reorder the terms: -13 + x = -13.453624047 Solving -13 + x = -13.453624047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -13.453624047 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.453624047 + 13 x = -13.453624047 + 13 Combine like terms: -13.453624047 + 13 = -0.453624047 x = -0.453624047 Simplifying x = -0.453624047Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.453624047, -0.453624047}Solution
x = {26.453624047, -0.453624047}
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