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Simplifying 13x2 + 17x = 117 Reorder the terms: 17x + 13x2 = 117 Solving 17x + 13x2 = 117 Solving for variable 'x'. Reorder the terms: -117 + 17x + 13x2 = 117 + -117 Combine like terms: 117 + -117 = 0 -117 + 17x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -9 + 1.307692308x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 1.307692308x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 1.307692308x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 1.307692308x + x2 = 0 + 9 1.307692308x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 1.307692308x + x2 = 9 The x term is 1.307692308x. Take half its coefficient (0.653846154). Square it (0.4275147931) and add it to both sides. Add '0.4275147931' to each side of the equation. 1.307692308x + 0.4275147931 + x2 = 9 + 0.4275147931 Reorder the terms: 0.4275147931 + 1.307692308x + x2 = 9 + 0.4275147931 Combine like terms: 9 + 0.4275147931 = 9.4275147931 0.4275147931 + 1.307692308x + x2 = 9.4275147931 Factor a perfect square on the left side: (x + 0.653846154)(x + 0.653846154) = 9.4275147931 Calculate the square root of the right side: 3.070425833 Break this problem into two subproblems by setting (x + 0.653846154) equal to 3.070425833 and -3.070425833.Subproblem 1
x + 0.653846154 = 3.070425833 Simplifying x + 0.653846154 = 3.070425833 Reorder the terms: 0.653846154 + x = 3.070425833 Solving 0.653846154 + x = 3.070425833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.653846154' to each side of the equation. 0.653846154 + -0.653846154 + x = 3.070425833 + -0.653846154 Combine like terms: 0.653846154 + -0.653846154 = 0.000000000 0.000000000 + x = 3.070425833 + -0.653846154 x = 3.070425833 + -0.653846154 Combine like terms: 3.070425833 + -0.653846154 = 2.416579679 x = 2.416579679 Simplifying x = 2.416579679Subproblem 2
x + 0.653846154 = -3.070425833 Simplifying x + 0.653846154 = -3.070425833 Reorder the terms: 0.653846154 + x = -3.070425833 Solving 0.653846154 + x = -3.070425833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.653846154' to each side of the equation. 0.653846154 + -0.653846154 + x = -3.070425833 + -0.653846154 Combine like terms: 0.653846154 + -0.653846154 = 0.000000000 0.000000000 + x = -3.070425833 + -0.653846154 x = -3.070425833 + -0.653846154 Combine like terms: -3.070425833 + -0.653846154 = -3.724271987 x = -3.724271987 Simplifying x = -3.724271987Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.416579679, -3.724271987}
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