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Simplifying 13x2 + -69x + -18 = 0 Reorder the terms: -18 + -69x + 13x2 = 0 Solving -18 + -69x + 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'. -1.384615385 + -5.307692308x + x2 = 0 Move the constant term to the right: Add '1.384615385' to each side of the equation. -1.384615385 + -5.307692308x + 1.384615385 + x2 = 0 + 1.384615385 Reorder the terms: -1.384615385 + 1.384615385 + -5.307692308x + x2 = 0 + 1.384615385 Combine like terms: -1.384615385 + 1.384615385 = 0.000000000 0.000000000 + -5.307692308x + x2 = 0 + 1.384615385 -5.307692308x + x2 = 0 + 1.384615385 Combine like terms: 0 + 1.384615385 = 1.384615385 -5.307692308x + x2 = 1.384615385 The x term is -5.307692308x. Take half its coefficient (-2.653846154). Square it (7.042899409) and add it to both sides. Add '7.042899409' to each side of the equation. -5.307692308x + 7.042899409 + x2 = 1.384615385 + 7.042899409 Reorder the terms: 7.042899409 + -5.307692308x + x2 = 1.384615385 + 7.042899409 Combine like terms: 1.384615385 + 7.042899409 = 8.427514794 7.042899409 + -5.307692308x + x2 = 8.427514794 Factor a perfect square on the left side: (x + -2.653846154)(x + -2.653846154) = 8.427514794 Calculate the square root of the right side: 2.903018221 Break this problem into two subproblems by setting (x + -2.653846154) equal to 2.903018221 and -2.903018221.Subproblem 1
x + -2.653846154 = 2.903018221 Simplifying x + -2.653846154 = 2.903018221 Reorder the terms: -2.653846154 + x = 2.903018221 Solving -2.653846154 + x = 2.903018221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.653846154' to each side of the equation. -2.653846154 + 2.653846154 + x = 2.903018221 + 2.653846154 Combine like terms: -2.653846154 + 2.653846154 = 0.000000000 0.000000000 + x = 2.903018221 + 2.653846154 x = 2.903018221 + 2.653846154 Combine like terms: 2.903018221 + 2.653846154 = 5.556864375 x = 5.556864375 Simplifying x = 5.556864375Subproblem 2
x + -2.653846154 = -2.903018221 Simplifying x + -2.653846154 = -2.903018221 Reorder the terms: -2.653846154 + x = -2.903018221 Solving -2.653846154 + x = -2.903018221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.653846154' to each side of the equation. -2.653846154 + 2.653846154 + x = -2.903018221 + 2.653846154 Combine like terms: -2.653846154 + 2.653846154 = 0.000000000 0.000000000 + x = -2.903018221 + 2.653846154 x = -2.903018221 + 2.653846154 Combine like terms: -2.903018221 + 2.653846154 = -0.249172067 x = -0.249172067 Simplifying x = -0.249172067Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.556864375, -0.249172067}
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