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Simplifying 42x2 + 137x + -125 = 0 Reorder the terms: -125 + 137x + 42x2 = 0 Solving -125 + 137x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -2.976190476 + 3.261904762x + x2 = 0 Move the constant term to the right: Add '2.976190476' to each side of the equation. -2.976190476 + 3.261904762x + 2.976190476 + x2 = 0 + 2.976190476 Reorder the terms: -2.976190476 + 2.976190476 + 3.261904762x + x2 = 0 + 2.976190476 Combine like terms: -2.976190476 + 2.976190476 = 0.000000000 0.000000000 + 3.261904762x + x2 = 0 + 2.976190476 3.261904762x + x2 = 0 + 2.976190476 Combine like terms: 0 + 2.976190476 = 2.976190476 3.261904762x + x2 = 2.976190476 The x term is 3.261904762x. Take half its coefficient (1.630952381). Square it (2.660005669) and add it to both sides. Add '2.660005669' to each side of the equation. 3.261904762x + 2.660005669 + x2 = 2.976190476 + 2.660005669 Reorder the terms: 2.660005669 + 3.261904762x + x2 = 2.976190476 + 2.660005669 Combine like terms: 2.976190476 + 2.660005669 = 5.636196145 2.660005669 + 3.261904762x + x2 = 5.636196145 Factor a perfect square on the left side: (x + 1.630952381)(x + 1.630952381) = 5.636196145 Calculate the square root of the right side: 2.374067426 Break this problem into two subproblems by setting (x + 1.630952381) equal to 2.374067426 and -2.374067426.Subproblem 1
x + 1.630952381 = 2.374067426 Simplifying x + 1.630952381 = 2.374067426 Reorder the terms: 1.630952381 + x = 2.374067426 Solving 1.630952381 + x = 2.374067426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.630952381' to each side of the equation. 1.630952381 + -1.630952381 + x = 2.374067426 + -1.630952381 Combine like terms: 1.630952381 + -1.630952381 = 0.000000000 0.000000000 + x = 2.374067426 + -1.630952381 x = 2.374067426 + -1.630952381 Combine like terms: 2.374067426 + -1.630952381 = 0.743115045 x = 0.743115045 Simplifying x = 0.743115045Subproblem 2
x + 1.630952381 = -2.374067426 Simplifying x + 1.630952381 = -2.374067426 Reorder the terms: 1.630952381 + x = -2.374067426 Solving 1.630952381 + x = -2.374067426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.630952381' to each side of the equation. 1.630952381 + -1.630952381 + x = -2.374067426 + -1.630952381 Combine like terms: 1.630952381 + -1.630952381 = 0.000000000 0.000000000 + x = -2.374067426 + -1.630952381 x = -2.374067426 + -1.630952381 Combine like terms: -2.374067426 + -1.630952381 = -4.005019807 x = -4.005019807 Simplifying x = -4.005019807Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.743115045, -4.005019807}
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