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Simplifying 3x2 + 10x + -12.75 = 0 Reorder the terms: -12.75 + 10x + 3x2 = 0 Solving -12.75 + 10x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.25 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + 3.333333333x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + 3.333333333x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + 3.333333333x + x2 = 0 + 4.25 3.333333333x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 3.333333333x + x2 = 4.25 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 4.25 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 4.25 + 2.777777779 Combine like terms: 4.25 + 2.777777779 = 7.027777779 2.777777779 + 3.333333333x + x2 = 7.027777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 7.027777779 Calculate the square root of the right side: 2.65099562 Break this problem into two subproblems by setting (x + 1.666666667) equal to 2.65099562 and -2.65099562.Subproblem 1
x + 1.666666667 = 2.65099562 Simplifying x + 1.666666667 = 2.65099562 Reorder the terms: 1.666666667 + x = 2.65099562 Solving 1.666666667 + x = 2.65099562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 2.65099562 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 2.65099562 + -1.666666667 x = 2.65099562 + -1.666666667 Combine like terms: 2.65099562 + -1.666666667 = 0.984328953 x = 0.984328953 Simplifying x = 0.984328953Subproblem 2
x + 1.666666667 = -2.65099562 Simplifying x + 1.666666667 = -2.65099562 Reorder the terms: 1.666666667 + x = -2.65099562 Solving 1.666666667 + x = -2.65099562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -2.65099562 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -2.65099562 + -1.666666667 x = -2.65099562 + -1.666666667 Combine like terms: -2.65099562 + -1.666666667 = -4.317662287 x = -4.317662287 Simplifying x = -4.317662287Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.984328953, -4.317662287}
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