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Simplifying 4x + 25 + 9x + 9 = 13x2 + -4x + 12 Reorder the terms: 25 + 9 + 4x + 9x = 13x2 + -4x + 12 Combine like terms: 25 + 9 = 34 34 + 4x + 9x = 13x2 + -4x + 12 Combine like terms: 4x + 9x = 13x 34 + 13x = 13x2 + -4x + 12 Reorder the terms: 34 + 13x = 12 + -4x + 13x2 Solving 34 + 13x = 12 + -4x + 13x2 Solving for variable 'x'. Reorder the terms: 34 + -12 + 13x + 4x + -13x2 = 12 + -4x + 13x2 + -12 + 4x + -13x2 Combine like terms: 34 + -12 = 22 22 + 13x + 4x + -13x2 = 12 + -4x + 13x2 + -12 + 4x + -13x2 Combine like terms: 13x + 4x = 17x 22 + 17x + -13x2 = 12 + -4x + 13x2 + -12 + 4x + -13x2 Reorder the terms: 22 + 17x + -13x2 = 12 + -12 + -4x + 4x + 13x2 + -13x2 Combine like terms: 12 + -12 = 0 22 + 17x + -13x2 = 0 + -4x + 4x + 13x2 + -13x2 22 + 17x + -13x2 = -4x + 4x + 13x2 + -13x2 Combine like terms: -4x + 4x = 0 22 + 17x + -13x2 = 0 + 13x2 + -13x2 22 + 17x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 22 + 17x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -1.692307692 + -1.307692308x + x2 = 0 Move the constant term to the right: Add '1.692307692' to each side of the equation. -1.692307692 + -1.307692308x + 1.692307692 + x2 = 0 + 1.692307692 Reorder the terms: -1.692307692 + 1.692307692 + -1.307692308x + x2 = 0 + 1.692307692 Combine like terms: -1.692307692 + 1.692307692 = 0.000000000 0.000000000 + -1.307692308x + x2 = 0 + 1.692307692 -1.307692308x + x2 = 0 + 1.692307692 Combine like terms: 0 + 1.692307692 = 1.692307692 -1.307692308x + x2 = 1.692307692 The x term is -1.307692308x. Take half its coefficient (-0.653846154). Square it (0.4275147931) and add it to both sides. Add '0.4275147931' to each side of the equation. -1.307692308x + 0.4275147931 + x2 = 1.692307692 + 0.4275147931 Reorder the terms: 0.4275147931 + -1.307692308x + x2 = 1.692307692 + 0.4275147931 Combine like terms: 1.692307692 + 0.4275147931 = 2.1198224851 0.4275147931 + -1.307692308x + x2 = 2.1198224851 Factor a perfect square on the left side: (x + -0.653846154)(x + -0.653846154) = 2.1198224851 Calculate the square root of the right side: 1.455961018 Break this problem into two subproblems by setting (x + -0.653846154) equal to 1.455961018 and -1.455961018.Subproblem 1
x + -0.653846154 = 1.455961018 Simplifying x + -0.653846154 = 1.455961018 Reorder the terms: -0.653846154 + x = 1.455961018 Solving -0.653846154 + x = 1.455961018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.653846154' to each side of the equation. -0.653846154 + 0.653846154 + x = 1.455961018 + 0.653846154 Combine like terms: -0.653846154 + 0.653846154 = 0.000000000 0.000000000 + x = 1.455961018 + 0.653846154 x = 1.455961018 + 0.653846154 Combine like terms: 1.455961018 + 0.653846154 = 2.109807172 x = 2.109807172 Simplifying x = 2.109807172Subproblem 2
x + -0.653846154 = -1.455961018 Simplifying x + -0.653846154 = -1.455961018 Reorder the terms: -0.653846154 + x = -1.455961018 Solving -0.653846154 + x = -1.455961018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.653846154' to each side of the equation. -0.653846154 + 0.653846154 + x = -1.455961018 + 0.653846154 Combine like terms: -0.653846154 + 0.653846154 = 0.000000000 0.000000000 + x = -1.455961018 + 0.653846154 x = -1.455961018 + 0.653846154 Combine like terms: -1.455961018 + 0.653846154 = -0.802114864 x = -0.802114864 Simplifying x = -0.802114864Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.109807172, -0.802114864}
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