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Simplifying 0.0795x2 + -0.902x + 1.781 = 0 Reorder the terms: 1.781 + -0.902x + 0.0795x2 = 0 Solving 1.781 + -0.902x + 0.0795x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0795 the coefficient of the squared term: Divide each side by '0.0795'. 22.40251572 + -11.34591195x + x2 = 0 Move the constant term to the right: Add '-22.40251572' to each side of the equation. 22.40251572 + -11.34591195x + -22.40251572 + x2 = 0 + -22.40251572 Reorder the terms: 22.40251572 + -22.40251572 + -11.34591195x + x2 = 0 + -22.40251572 Combine like terms: 22.40251572 + -22.40251572 = 0.00000000 0.00000000 + -11.34591195x + x2 = 0 + -22.40251572 -11.34591195x + x2 = 0 + -22.40251572 Combine like terms: 0 + -22.40251572 = -22.40251572 -11.34591195x + x2 = -22.40251572 The x term is -11.34591195x. Take half its coefficient (-5.672955975). Square it (32.18242949) and add it to both sides. Add '32.18242949' to each side of the equation. -11.34591195x + 32.18242949 + x2 = -22.40251572 + 32.18242949 Reorder the terms: 32.18242949 + -11.34591195x + x2 = -22.40251572 + 32.18242949 Combine like terms: -22.40251572 + 32.18242949 = 9.77991377 32.18242949 + -11.34591195x + x2 = 9.77991377 Factor a perfect square on the left side: (x + -5.672955975)(x + -5.672955975) = 9.77991377 Calculate the square root of the right side: 3.127285368 Break this problem into two subproblems by setting (x + -5.672955975) equal to 3.127285368 and -3.127285368.Subproblem 1
x + -5.672955975 = 3.127285368 Simplifying x + -5.672955975 = 3.127285368 Reorder the terms: -5.672955975 + x = 3.127285368 Solving -5.672955975 + x = 3.127285368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.672955975' to each side of the equation. -5.672955975 + 5.672955975 + x = 3.127285368 + 5.672955975 Combine like terms: -5.672955975 + 5.672955975 = 0.000000000 0.000000000 + x = 3.127285368 + 5.672955975 x = 3.127285368 + 5.672955975 Combine like terms: 3.127285368 + 5.672955975 = 8.800241343 x = 8.800241343 Simplifying x = 8.800241343Subproblem 2
x + -5.672955975 = -3.127285368 Simplifying x + -5.672955975 = -3.127285368 Reorder the terms: -5.672955975 + x = -3.127285368 Solving -5.672955975 + x = -3.127285368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.672955975' to each side of the equation. -5.672955975 + 5.672955975 + x = -3.127285368 + 5.672955975 Combine like terms: -5.672955975 + 5.672955975 = 0.000000000 0.000000000 + x = -3.127285368 + 5.672955975 x = -3.127285368 + 5.672955975 Combine like terms: -3.127285368 + 5.672955975 = 2.545670607 x = 2.545670607 Simplifying x = 2.545670607Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.800241343, 2.545670607}
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