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Simplifying -0.415x2 + -0.33x + 1 = 0 Reorder the terms: 1 + -0.33x + -0.415x2 = 0 Solving 1 + -0.33x + -0.415x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.415 the coefficient of the squared term: Divide each side by '-0.415'. -2.409638554 + 0.7951807229x + x2 = 0 Move the constant term to the right: Add '2.409638554' to each side of the equation. -2.409638554 + 0.7951807229x + 2.409638554 + x2 = 0 + 2.409638554 Reorder the terms: -2.409638554 + 2.409638554 + 0.7951807229x + x2 = 0 + 2.409638554 Combine like terms: -2.409638554 + 2.409638554 = 0.000000000 0.000000000 + 0.7951807229x + x2 = 0 + 2.409638554 0.7951807229x + x2 = 0 + 2.409638554 Combine like terms: 0 + 2.409638554 = 2.409638554 0.7951807229x + x2 = 2.409638554 The x term is 0.7951807229x. Take half its coefficient (0.3975903615). Square it (0.1580780956) and add it to both sides. Add '0.1580780956' to each side of the equation. 0.7951807229x + 0.1580780956 + x2 = 2.409638554 + 0.1580780956 Reorder the terms: 0.1580780956 + 0.7951807229x + x2 = 2.409638554 + 0.1580780956 Combine like terms: 2.409638554 + 0.1580780956 = 2.5677166496 0.1580780956 + 0.7951807229x + x2 = 2.5677166496 Factor a perfect square on the left side: (x + 0.3975903615)(x + 0.3975903615) = 2.5677166496 Calculate the square root of the right side: 1.602409639 Break this problem into two subproblems by setting (x + 0.3975903615) equal to 1.602409639 and -1.602409639.Subproblem 1
x + 0.3975903615 = 1.602409639 Simplifying x + 0.3975903615 = 1.602409639 Reorder the terms: 0.3975903615 + x = 1.602409639 Solving 0.3975903615 + x = 1.602409639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3975903615' to each side of the equation. 0.3975903615 + -0.3975903615 + x = 1.602409639 + -0.3975903615 Combine like terms: 0.3975903615 + -0.3975903615 = 0.0000000000 0.0000000000 + x = 1.602409639 + -0.3975903615 x = 1.602409639 + -0.3975903615 Combine like terms: 1.602409639 + -0.3975903615 = 1.2048192775 x = 1.2048192775 Simplifying x = 1.2048192775Subproblem 2
x + 0.3975903615 = -1.602409639 Simplifying x + 0.3975903615 = -1.602409639 Reorder the terms: 0.3975903615 + x = -1.602409639 Solving 0.3975903615 + x = -1.602409639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3975903615' to each side of the equation. 0.3975903615 + -0.3975903615 + x = -1.602409639 + -0.3975903615 Combine like terms: 0.3975903615 + -0.3975903615 = 0.0000000000 0.0000000000 + x = -1.602409639 + -0.3975903615 x = -1.602409639 + -0.3975903615 Combine like terms: -1.602409639 + -0.3975903615 = -2.0000000005 x = -2.0000000005 Simplifying x = -2.0000000005Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2048192775, -2.0000000005}
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