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Simplifying 7x2 + 29x + -4 = 0 Reorder the terms: -4 + 29x + 7x2 = 0 Solving -4 + 29x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 4.142857143x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 4.142857143x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 4.142857143x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 4.142857143x + x2 = 0 + 0.5714285714 4.142857143x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 4.142857143x + x2 = 0.5714285714 The x term is 4.142857143x. Take half its coefficient (2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. 4.142857143x + 4.290816329 + x2 = 0.5714285714 + 4.290816329 Reorder the terms: 4.290816329 + 4.142857143x + x2 = 0.5714285714 + 4.290816329 Combine like terms: 0.5714285714 + 4.290816329 = 4.8622449004 4.290816329 + 4.142857143x + x2 = 4.8622449004 Factor a perfect square on the left side: (x + 2.071428572)(x + 2.071428572) = 4.8622449004 Calculate the square root of the right side: 2.205049863 Break this problem into two subproblems by setting (x + 2.071428572) equal to 2.205049863 and -2.205049863.Subproblem 1
x + 2.071428572 = 2.205049863 Simplifying x + 2.071428572 = 2.205049863 Reorder the terms: 2.071428572 + x = 2.205049863 Solving 2.071428572 + x = 2.205049863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + x = 2.205049863 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = 2.205049863 + -2.071428572 x = 2.205049863 + -2.071428572 Combine like terms: 2.205049863 + -2.071428572 = 0.133621291 x = 0.133621291 Simplifying x = 0.133621291Subproblem 2
x + 2.071428572 = -2.205049863 Simplifying x + 2.071428572 = -2.205049863 Reorder the terms: 2.071428572 + x = -2.205049863 Solving 2.071428572 + x = -2.205049863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + x = -2.205049863 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = -2.205049863 + -2.071428572 x = -2.205049863 + -2.071428572 Combine like terms: -2.205049863 + -2.071428572 = -4.276478435 x = -4.276478435 Simplifying x = -4.276478435Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.133621291, -4.276478435}
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