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Simplifying 49x2 + -42x = 285 Reorder the terms: -42x + 49x2 = 285 Solving -42x + 49x2 = 285 Solving for variable 'x'. Reorder the terms: -285 + -42x + 49x2 = 285 + -285 Combine like terms: 285 + -285 = 0 -285 + -42x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -5.816326531 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '5.816326531' to each side of the equation. -5.816326531 + -0.8571428571x + 5.816326531 + x2 = 0 + 5.816326531 Reorder the terms: -5.816326531 + 5.816326531 + -0.8571428571x + x2 = 0 + 5.816326531 Combine like terms: -5.816326531 + 5.816326531 = 0.000000000 0.000000000 + -0.8571428571x + x2 = 0 + 5.816326531 -0.8571428571x + x2 = 0 + 5.816326531 Combine like terms: 0 + 5.816326531 = 5.816326531 -0.8571428571x + x2 = 5.816326531 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 5.816326531 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 5.816326531 + 0.1836734694 Combine like terms: 5.816326531 + 0.1836734694 = 6.0000000004 0.1836734694 + -0.8571428571x + x2 = 6.0000000004 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 6.0000000004 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -0.4285714286 = 2.449489743 Simplifying x + -0.4285714286 = 2.449489743 Reorder the terms: -0.4285714286 + x = 2.449489743 Solving -0.4285714286 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 2.449489743 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 2.449489743 + 0.4285714286 x = 2.449489743 + 0.4285714286 Combine like terms: 2.449489743 + 0.4285714286 = 2.8780611716 x = 2.8780611716 Simplifying x = 2.8780611716Subproblem 2
x + -0.4285714286 = -2.449489743 Simplifying x + -0.4285714286 = -2.449489743 Reorder the terms: -0.4285714286 + x = -2.449489743 Solving -0.4285714286 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -2.449489743 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -2.449489743 + 0.4285714286 x = -2.449489743 + 0.4285714286 Combine like terms: -2.449489743 + 0.4285714286 = -2.0209183144 x = -2.0209183144 Simplifying x = -2.0209183144Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8780611716, -2.0209183144}
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