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Simplifying -11x2 + -2x + -8x2 + 3 + 15x = 0 Reorder the terms: 3 + -2x + 15x + -11x2 + -8x2 = 0 Combine like terms: -2x + 15x = 13x 3 + 13x + -11x2 + -8x2 = 0 Combine like terms: -11x2 + -8x2 = -19x2 3 + 13x + -19x2 = 0 Solving 3 + 13x + -19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -0.1578947368 + -0.6842105263x + x2 = 0 Move the constant term to the right: Add '0.1578947368' to each side of the equation. -0.1578947368 + -0.6842105263x + 0.1578947368 + x2 = 0 + 0.1578947368 Reorder the terms: -0.1578947368 + 0.1578947368 + -0.6842105263x + x2 = 0 + 0.1578947368 Combine like terms: -0.1578947368 + 0.1578947368 = 0.0000000000 0.0000000000 + -0.6842105263x + x2 = 0 + 0.1578947368 -0.6842105263x + x2 = 0 + 0.1578947368 Combine like terms: 0 + 0.1578947368 = 0.1578947368 -0.6842105263x + x2 = 0.1578947368 The x term is -0.6842105263x. Take half its coefficient (-0.3421052632). Square it (0.1170360111) and add it to both sides. Add '0.1170360111' to each side of the equation. -0.6842105263x + 0.1170360111 + x2 = 0.1578947368 + 0.1170360111 Reorder the terms: 0.1170360111 + -0.6842105263x + x2 = 0.1578947368 + 0.1170360111 Combine like terms: 0.1578947368 + 0.1170360111 = 0.2749307479 0.1170360111 + -0.6842105263x + x2 = 0.2749307479 Factor a perfect square on the left side: (x + -0.3421052632)(x + -0.3421052632) = 0.2749307479 Calculate the square root of the right side: 0.524338391 Break this problem into two subproblems by setting (x + -0.3421052632) equal to 0.524338391 and -0.524338391.Subproblem 1
x + -0.3421052632 = 0.524338391 Simplifying x + -0.3421052632 = 0.524338391 Reorder the terms: -0.3421052632 + x = 0.524338391 Solving -0.3421052632 + x = 0.524338391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3421052632' to each side of the equation. -0.3421052632 + 0.3421052632 + x = 0.524338391 + 0.3421052632 Combine like terms: -0.3421052632 + 0.3421052632 = 0.0000000000 0.0000000000 + x = 0.524338391 + 0.3421052632 x = 0.524338391 + 0.3421052632 Combine like terms: 0.524338391 + 0.3421052632 = 0.8664436542 x = 0.8664436542 Simplifying x = 0.8664436542Subproblem 2
x + -0.3421052632 = -0.524338391 Simplifying x + -0.3421052632 = -0.524338391 Reorder the terms: -0.3421052632 + x = -0.524338391 Solving -0.3421052632 + x = -0.524338391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3421052632' to each side of the equation. -0.3421052632 + 0.3421052632 + x = -0.524338391 + 0.3421052632 Combine like terms: -0.3421052632 + 0.3421052632 = 0.0000000000 0.0000000000 + x = -0.524338391 + 0.3421052632 x = -0.524338391 + 0.3421052632 Combine like terms: -0.524338391 + 0.3421052632 = -0.1822331278 x = -0.1822331278 Simplifying x = -0.1822331278Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8664436542, -0.1822331278}
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