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Simplifying 13x2 + -3x + -56 = 0 Reorder the terms: -56 + -3x + 13x2 = 0 Solving -56 + -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'. -4.307692308 + -0.2307692308x + x2 = 0 Move the constant term to the right: Add '4.307692308' to each side of the equation. -4.307692308 + -0.2307692308x + 4.307692308 + x2 = 0 + 4.307692308 Reorder the terms: -4.307692308 + 4.307692308 + -0.2307692308x + x2 = 0 + 4.307692308 Combine like terms: -4.307692308 + 4.307692308 = 0.000000000 0.000000000 + -0.2307692308x + x2 = 0 + 4.307692308 -0.2307692308x + x2 = 0 + 4.307692308 Combine like terms: 0 + 4.307692308 = 4.307692308 -0.2307692308x + x2 = 4.307692308 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 = 4.307692308 + 0.01331360947 Reorder the terms: 0.01331360947 + -0.2307692308x + x2 = 4.307692308 + 0.01331360947 Combine like terms: 4.307692308 + 0.01331360947 = 4.32100591747 0.01331360947 + -0.2307692308x + x2 = 4.32100591747 Factor a perfect square on the left side: (x + -0.1153846154)(x + -0.1153846154) = 4.32100591747 Calculate the square root of the right side: 2.078702941 Break this problem into two subproblems by setting (x + -0.1153846154) equal to 2.078702941 and -2.078702941.Subproblem 1
x + -0.1153846154 = 2.078702941 Simplifying x + -0.1153846154 = 2.078702941 Reorder the terms: -0.1153846154 + x = 2.078702941 Solving -0.1153846154 + x = 2.078702941 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 = 2.078702941 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = 2.078702941 + 0.1153846154 x = 2.078702941 + 0.1153846154 Combine like terms: 2.078702941 + 0.1153846154 = 2.1940875564 x = 2.1940875564 Simplifying x = 2.1940875564Subproblem 2
x + -0.1153846154 = -2.078702941 Simplifying x + -0.1153846154 = -2.078702941 Reorder the terms: -0.1153846154 + x = -2.078702941 Solving -0.1153846154 + x = -2.078702941 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 = -2.078702941 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = -2.078702941 + 0.1153846154 x = -2.078702941 + 0.1153846154 Combine like terms: -2.078702941 + 0.1153846154 = -1.9633183256 x = -1.9633183256 Simplifying x = -1.9633183256Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1940875564, -1.9633183256}
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