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Simplifying 13x2 + -3x + -4 = 0 Reorder the terms: -4 + -3x + 13x2 = 0 Solving -4 + -3x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.3076923077 + -0.2307692308x + x2 = 0 Move the constant term to the right: Add '0.3076923077' to each side of the equation. -0.3076923077 + -0.2307692308x + 0.3076923077 + x2 = 0 + 0.3076923077 Reorder the terms: -0.3076923077 + 0.3076923077 + -0.2307692308x + x2 = 0 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + -0.2307692308x + x2 = 0 + 0.3076923077 -0.2307692308x + x2 = 0 + 0.3076923077 Combine like terms: 0 + 0.3076923077 = 0.3076923077 -0.2307692308x + x2 = 0.3076923077 The x term is -0.2307692308x. Take half its coefficient (-0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. -0.2307692308x + 0.01331360947 + x2 = 0.3076923077 + 0.01331360947 Reorder the terms: 0.01331360947 + -0.2307692308x + x2 = 0.3076923077 + 0.01331360947 Combine like terms: 0.3076923077 + 0.01331360947 = 0.32100591717 0.01331360947 + -0.2307692308x + x2 = 0.32100591717 Factor a perfect square on the left side: (x + -0.1153846154)(x + -0.1153846154) = 0.32100591717 Calculate the square root of the right side: 0.566573841 Break this problem into two subproblems by setting (x + -0.1153846154) equal to 0.566573841 and -0.566573841.Subproblem 1
x + -0.1153846154 = 0.566573841 Simplifying x + -0.1153846154 = 0.566573841 Reorder the terms: -0.1153846154 + x = 0.566573841 Solving -0.1153846154 + x = 0.566573841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + x = 0.566573841 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = 0.566573841 + 0.1153846154 x = 0.566573841 + 0.1153846154 Combine like terms: 0.566573841 + 0.1153846154 = 0.6819584564 x = 0.6819584564 Simplifying x = 0.6819584564Subproblem 2
x + -0.1153846154 = -0.566573841 Simplifying x + -0.1153846154 = -0.566573841 Reorder the terms: -0.1153846154 + x = -0.566573841 Solving -0.1153846154 + x = -0.566573841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + x = -0.566573841 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = -0.566573841 + 0.1153846154 x = -0.566573841 + 0.1153846154 Combine like terms: -0.566573841 + 0.1153846154 = -0.4511892256 x = -0.4511892256 Simplifying x = -0.4511892256Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6819584564, -0.4511892256}
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