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Simplifying 7x2 = 29x + 4 Reorder the terms: 7x2 = 4 + 29x Solving 7x2 = 4 + 29x Solving for variable 'x'. Reorder the terms: -4 + -29x + 7x2 = 4 + 29x + -4 + -29x Reorder the terms: -4 + -29x + 7x2 = 4 + -4 + 29x + -29x Combine like terms: 4 + -4 = 0 -4 + -29x + 7x2 = 0 + 29x + -29x -4 + -29x + 7x2 = 29x + -29x Combine like terms: 29x + -29x = 0 -4 + -29x + 7x2 = 0 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 = 4.276478435 x = 4.276478435 Simplifying x = 4.276478435Subproblem 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 = -0.133621291 x = -0.133621291 Simplifying x = -0.133621291Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.276478435, -0.133621291}
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