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Simplifying -10x2 + -4x + -9x2 + 5 + 7x = 0 Reorder the terms: 5 + -4x + 7x + -10x2 + -9x2 = 0 Combine like terms: -4x + 7x = 3x 5 + 3x + -10x2 + -9x2 = 0 Combine like terms: -10x2 + -9x2 = -19x2 5 + 3x + -19x2 = 0 Solving 5 + 3x + -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 + -0.1578947368x + x2 = 0 Move the constant term to the right: Add '0.2631578947' to each side of the equation. -0.2631578947 + -0.1578947368x + 0.2631578947 + x2 = 0 + 0.2631578947 Reorder the terms: -0.2631578947 + 0.2631578947 + -0.1578947368x + x2 = 0 + 0.2631578947 Combine like terms: -0.2631578947 + 0.2631578947 = 0.0000000000 0.0000000000 + -0.1578947368x + x2 = 0 + 0.2631578947 -0.1578947368x + x2 = 0 + 0.2631578947 Combine like terms: 0 + 0.2631578947 = 0.2631578947 -0.1578947368x + x2 = 0.2631578947 The x term is -0.1578947368x. Take half its coefficient (-0.0789473684). Square it (0.006232686977) and add it to both sides. Add '0.006232686977' to each side of the equation. -0.1578947368x + 0.006232686977 + x2 = 0.2631578947 + 0.006232686977 Reorder the terms: 0.006232686977 + -0.1578947368x + x2 = 0.2631578947 + 0.006232686977 Combine like terms: 0.2631578947 + 0.006232686977 = 0.269390581677 0.006232686977 + -0.1578947368x + x2 = 0.269390581677 Factor a perfect square on the left side: (x + -0.0789473684)(x + -0.0789473684) = 0.269390581677 Calculate the square root of the right side: 0.519028498 Break this problem into two subproblems by setting (x + -0.0789473684) equal to 0.519028498 and -0.519028498.Subproblem 1
x + -0.0789473684 = 0.519028498 Simplifying x + -0.0789473684 = 0.519028498 Reorder the terms: -0.0789473684 + x = 0.519028498 Solving -0.0789473684 + x = 0.519028498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0789473684' to each side of the equation. -0.0789473684 + 0.0789473684 + x = 0.519028498 + 0.0789473684 Combine like terms: -0.0789473684 + 0.0789473684 = 0.0000000000 0.0000000000 + x = 0.519028498 + 0.0789473684 x = 0.519028498 + 0.0789473684 Combine like terms: 0.519028498 + 0.0789473684 = 0.5979758664 x = 0.5979758664 Simplifying x = 0.5979758664Subproblem 2
x + -0.0789473684 = -0.519028498 Simplifying x + -0.0789473684 = -0.519028498 Reorder the terms: -0.0789473684 + x = -0.519028498 Solving -0.0789473684 + x = -0.519028498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0789473684' to each side of the equation. -0.0789473684 + 0.0789473684 + x = -0.519028498 + 0.0789473684 Combine like terms: -0.0789473684 + 0.0789473684 = 0.0000000000 0.0000000000 + x = -0.519028498 + 0.0789473684 x = -0.519028498 + 0.0789473684 Combine like terms: -0.519028498 + 0.0789473684 = -0.4400811296 x = -0.4400811296 Simplifying x = -0.4400811296Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5979758664, -0.4400811296}
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