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Simplifying 69x2 + 96x + -190 = 0 Reorder the terms: -190 + 96x + 69x2 = 0 Solving -190 + 96x + 69x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 69 the coefficient of the squared term: Divide each side by '69'. -2.753623188 + 1.391304348x + x2 = 0 Move the constant term to the right: Add '2.753623188' to each side of the equation. -2.753623188 + 1.391304348x + 2.753623188 + x2 = 0 + 2.753623188 Reorder the terms: -2.753623188 + 2.753623188 + 1.391304348x + x2 = 0 + 2.753623188 Combine like terms: -2.753623188 + 2.753623188 = 0.000000000 0.000000000 + 1.391304348x + x2 = 0 + 2.753623188 1.391304348x + x2 = 0 + 2.753623188 Combine like terms: 0 + 2.753623188 = 2.753623188 1.391304348x + x2 = 2.753623188 The x term is 1.391304348x. Take half its coefficient (0.695652174). Square it (0.4839319472) and add it to both sides. Add '0.4839319472' to each side of the equation. 1.391304348x + 0.4839319472 + x2 = 2.753623188 + 0.4839319472 Reorder the terms: 0.4839319472 + 1.391304348x + x2 = 2.753623188 + 0.4839319472 Combine like terms: 2.753623188 + 0.4839319472 = 3.2375551352 0.4839319472 + 1.391304348x + x2 = 3.2375551352 Factor a perfect square on the left side: (x + 0.695652174)(x + 0.695652174) = 3.2375551352 Calculate the square root of the right side: 1.799320743 Break this problem into two subproblems by setting (x + 0.695652174) equal to 1.799320743 and -1.799320743.Subproblem 1
x + 0.695652174 = 1.799320743 Simplifying x + 0.695652174 = 1.799320743 Reorder the terms: 0.695652174 + x = 1.799320743 Solving 0.695652174 + x = 1.799320743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.695652174' to each side of the equation. 0.695652174 + -0.695652174 + x = 1.799320743 + -0.695652174 Combine like terms: 0.695652174 + -0.695652174 = 0.000000000 0.000000000 + x = 1.799320743 + -0.695652174 x = 1.799320743 + -0.695652174 Combine like terms: 1.799320743 + -0.695652174 = 1.103668569 x = 1.103668569 Simplifying x = 1.103668569Subproblem 2
x + 0.695652174 = -1.799320743 Simplifying x + 0.695652174 = -1.799320743 Reorder the terms: 0.695652174 + x = -1.799320743 Solving 0.695652174 + x = -1.799320743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.695652174' to each side of the equation. 0.695652174 + -0.695652174 + x = -1.799320743 + -0.695652174 Combine like terms: 0.695652174 + -0.695652174 = 0.000000000 0.000000000 + x = -1.799320743 + -0.695652174 x = -1.799320743 + -0.695652174 Combine like terms: -1.799320743 + -0.695652174 = -2.494972917 x = -2.494972917 Simplifying x = -2.494972917Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.103668569, -2.494972917}
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