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Simplifying 49x2 + -84x + 30 = 0 Reorder the terms: 30 + -84x + 49x2 = 0 Solving 30 + -84x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.612244898 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '-0.612244898' to each side of the equation. 0.612244898 + -1.714285714x + -0.612244898 + x2 = 0 + -0.612244898 Reorder the terms: 0.612244898 + -0.612244898 + -1.714285714x + x2 = 0 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + -1.714285714x + x2 = 0 + -0.612244898 -1.714285714x + x2 = 0 + -0.612244898 Combine like terms: 0 + -0.612244898 = -0.612244898 -1.714285714x + x2 = -0.612244898 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 = -0.612244898 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = -0.612244898 + 0.7346938773 Combine like terms: -0.612244898 + 0.7346938773 = 0.1224489793 0.7346938773 + -1.714285714x + x2 = 0.1224489793 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 0.1224489793 Calculate the square root of the right side: 0.349927106 Break this problem into two subproblems by setting (x + -0.857142857) equal to 0.349927106 and -0.349927106.Subproblem 1
x + -0.857142857 = 0.349927106 Simplifying x + -0.857142857 = 0.349927106 Reorder the terms: -0.857142857 + x = 0.349927106 Solving -0.857142857 + x = 0.349927106 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 = 0.349927106 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 0.349927106 + 0.857142857 x = 0.349927106 + 0.857142857 Combine like terms: 0.349927106 + 0.857142857 = 1.207069963 x = 1.207069963 Simplifying x = 1.207069963Subproblem 2
x + -0.857142857 = -0.349927106 Simplifying x + -0.857142857 = -0.349927106 Reorder the terms: -0.857142857 + x = -0.349927106 Solving -0.857142857 + x = -0.349927106 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 = -0.349927106 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -0.349927106 + 0.857142857 x = -0.349927106 + 0.857142857 Combine like terms: -0.349927106 + 0.857142857 = 0.507215751 x = 0.507215751 Simplifying x = 0.507215751Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.207069963, 0.507215751}
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