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Simplifying 49x2 + -84x = -29 Reorder the terms: -84x + 49x2 = -29 Solving -84x + 49x2 = -29 Solving for variable 'x'. Reorder the terms: 29 + -84x + 49x2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + -84x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.5918367347 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '-0.5918367347' to each side of the equation. 0.5918367347 + -1.714285714x + -0.5918367347 + x2 = 0 + -0.5918367347 Reorder the terms: 0.5918367347 + -0.5918367347 + -1.714285714x + x2 = 0 + -0.5918367347 Combine like terms: 0.5918367347 + -0.5918367347 = 0.0000000000 0.0000000000 + -1.714285714x + x2 = 0 + -0.5918367347 -1.714285714x + x2 = 0 + -0.5918367347 Combine like terms: 0 + -0.5918367347 = -0.5918367347 -1.714285714x + x2 = -0.5918367347 The x term is -1.714285714x. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714x + 0.7346938773 + x2 = -0.5918367347 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = -0.5918367347 + 0.7346938773 Combine like terms: -0.5918367347 + 0.7346938773 = 0.1428571426 0.7346938773 + -1.714285714x + x2 = 0.1428571426 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 0.1428571426 Calculate the square root of the right side: 0.377964473 Break this problem into two subproblems by setting (x + -0.857142857) equal to 0.377964473 and -0.377964473.Subproblem 1
x + -0.857142857 = 0.377964473 Simplifying x + -0.857142857 = 0.377964473 Reorder the terms: -0.857142857 + x = 0.377964473 Solving -0.857142857 + x = 0.377964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 0.377964473 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 0.377964473 + 0.857142857 x = 0.377964473 + 0.857142857 Combine like terms: 0.377964473 + 0.857142857 = 1.23510733 x = 1.23510733 Simplifying x = 1.23510733Subproblem 2
x + -0.857142857 = -0.377964473 Simplifying x + -0.857142857 = -0.377964473 Reorder the terms: -0.857142857 + x = -0.377964473 Solving -0.857142857 + x = -0.377964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -0.377964473 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -0.377964473 + 0.857142857 x = -0.377964473 + 0.857142857 Combine like terms: -0.377964473 + 0.857142857 = 0.479178384 x = 0.479178384 Simplifying x = 0.479178384Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.23510733, 0.479178384}
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