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Simplifying -10x2 + 2x + -9x2 + 5 = 0 Reorder the terms: 5 + 2x + -10x2 + -9x2 = 0 Combine like terms: -10x2 + -9x2 = -19x2 5 + 2x + -19x2 = 0 Solving 5 + 2x + -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'. -0.2631578947 + -0.1052631579x + x2 = 0 Move the constant term to the right: Add '0.2631578947' to each side of the equation. -0.2631578947 + -0.1052631579x + 0.2631578947 + x2 = 0 + 0.2631578947 Reorder the terms: -0.2631578947 + 0.2631578947 + -0.1052631579x + x2 = 0 + 0.2631578947 Combine like terms: -0.2631578947 + 0.2631578947 = 0.0000000000 0.0000000000 + -0.1052631579x + x2 = 0 + 0.2631578947 -0.1052631579x + x2 = 0 + 0.2631578947 Combine like terms: 0 + 0.2631578947 = 0.2631578947 -0.1052631579x + x2 = 0.2631578947 The x term is -0.1052631579x. Take half its coefficient (-0.05263157895). Square it (0.002770083103) and add it to both sides. Add '0.002770083103' to each side of the equation. -0.1052631579x + 0.002770083103 + x2 = 0.2631578947 + 0.002770083103 Reorder the terms: 0.002770083103 + -0.1052631579x + x2 = 0.2631578947 + 0.002770083103 Combine like terms: 0.2631578947 + 0.002770083103 = 0.265927977803 0.002770083103 + -0.1052631579x + x2 = 0.265927977803 Factor a perfect square on the left side: (x + -0.05263157895)(x + -0.05263157895) = 0.265927977803 Calculate the square root of the right side: 0.515682051 Break this problem into two subproblems by setting (x + -0.05263157895) equal to 0.515682051 and -0.515682051.Subproblem 1
x + -0.05263157895 = 0.515682051 Simplifying x + -0.05263157895 = 0.515682051 Reorder the terms: -0.05263157895 + x = 0.515682051 Solving -0.05263157895 + x = 0.515682051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05263157895' to each side of the equation. -0.05263157895 + 0.05263157895 + x = 0.515682051 + 0.05263157895 Combine like terms: -0.05263157895 + 0.05263157895 = 0.00000000000 0.00000000000 + x = 0.515682051 + 0.05263157895 x = 0.515682051 + 0.05263157895 Combine like terms: 0.515682051 + 0.05263157895 = 0.56831362995 x = 0.56831362995 Simplifying x = 0.56831362995Subproblem 2
x + -0.05263157895 = -0.515682051 Simplifying x + -0.05263157895 = -0.515682051 Reorder the terms: -0.05263157895 + x = -0.515682051 Solving -0.05263157895 + x = -0.515682051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05263157895' to each side of the equation. -0.05263157895 + 0.05263157895 + x = -0.515682051 + 0.05263157895 Combine like terms: -0.05263157895 + 0.05263157895 = 0.00000000000 0.00000000000 + x = -0.515682051 + 0.05263157895 x = -0.515682051 + 0.05263157895 Combine like terms: -0.515682051 + 0.05263157895 = -0.46305047205 x = -0.46305047205 Simplifying x = -0.46305047205Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.56831362995, -0.46305047205}
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