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Simplifying 13x2 + 15 = 104x Reorder the terms: 15 + 13x2 = 104x Solving 15 + 13x2 = 104x Solving for variable 'x'. Reorder the terms: 15 + -104x + 13x2 = 104x + -104x Combine like terms: 104x + -104x = 0 15 + -104x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 1.153846154 + -8x + x2 = 0 Move the constant term to the right: Add '-1.153846154' to each side of the equation. 1.153846154 + -8x + -1.153846154 + x2 = 0 + -1.153846154 Reorder the terms: 1.153846154 + -1.153846154 + -8x + x2 = 0 + -1.153846154 Combine like terms: 1.153846154 + -1.153846154 = 0.000000000 0.000000000 + -8x + x2 = 0 + -1.153846154 -8x + x2 = 0 + -1.153846154 Combine like terms: 0 + -1.153846154 = -1.153846154 -8x + x2 = -1.153846154 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -1.153846154 + 16 Reorder the terms: 16 + -8x + x2 = -1.153846154 + 16 Combine like terms: -1.153846154 + 16 = 14.846153846 16 + -8x + x2 = 14.846153846 Factor a perfect square on the left side: (x + -4)(x + -4) = 14.846153846 Calculate the square root of the right side: 3.853070703 Break this problem into two subproblems by setting (x + -4) equal to 3.853070703 and -3.853070703.Subproblem 1
x + -4 = 3.853070703 Simplifying x + -4 = 3.853070703 Reorder the terms: -4 + x = 3.853070703 Solving -4 + x = 3.853070703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.853070703 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.853070703 + 4 x = 3.853070703 + 4 Combine like terms: 3.853070703 + 4 = 7.853070703 x = 7.853070703 Simplifying x = 7.853070703Subproblem 2
x + -4 = -3.853070703 Simplifying x + -4 = -3.853070703 Reorder the terms: -4 + x = -3.853070703 Solving -4 + x = -3.853070703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.853070703 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.853070703 + 4 x = -3.853070703 + 4 Combine like terms: -3.853070703 + 4 = 0.146929297 x = 0.146929297 Simplifying x = 0.146929297Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.853070703, 0.146929297}
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