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Simplifying -1.3x2 + 4x + 1.75 = 0 Reorder the terms: 1.75 + 4x + -1.3x2 = 0 Solving 1.75 + 4x + -1.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.3 the coefficient of the squared term: Divide each side by '-1.3'. -1.346153846 + -3.076923077x + x2 = 0 Move the constant term to the right: Add '1.346153846' to each side of the equation. -1.346153846 + -3.076923077x + 1.346153846 + x2 = 0 + 1.346153846 Reorder the terms: -1.346153846 + 1.346153846 + -3.076923077x + x2 = 0 + 1.346153846 Combine like terms: -1.346153846 + 1.346153846 = 0.000000000 0.000000000 + -3.076923077x + x2 = 0 + 1.346153846 -3.076923077x + x2 = 0 + 1.346153846 Combine like terms: 0 + 1.346153846 = 1.346153846 -3.076923077x + x2 = 1.346153846 The x term is -3.076923077x. Take half its coefficient (-1.538461539). Square it (2.366863907) and add it to both sides. Add '2.366863907' to each side of the equation. -3.076923077x + 2.366863907 + x2 = 1.346153846 + 2.366863907 Reorder the terms: 2.366863907 + -3.076923077x + x2 = 1.346153846 + 2.366863907 Combine like terms: 1.346153846 + 2.366863907 = 3.713017753 2.366863907 + -3.076923077x + x2 = 3.713017753 Factor a perfect square on the left side: (x + -1.538461539)(x + -1.538461539) = 3.713017753 Calculate the square root of the right side: 1.926919239 Break this problem into two subproblems by setting (x + -1.538461539) equal to 1.926919239 and -1.926919239.Subproblem 1
x + -1.538461539 = 1.926919239 Simplifying x + -1.538461539 = 1.926919239 Reorder the terms: -1.538461539 + x = 1.926919239 Solving -1.538461539 + x = 1.926919239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.538461539' to each side of the equation. -1.538461539 + 1.538461539 + x = 1.926919239 + 1.538461539 Combine like terms: -1.538461539 + 1.538461539 = 0.000000000 0.000000000 + x = 1.926919239 + 1.538461539 x = 1.926919239 + 1.538461539 Combine like terms: 1.926919239 + 1.538461539 = 3.465380778 x = 3.465380778 Simplifying x = 3.465380778Subproblem 2
x + -1.538461539 = -1.926919239 Simplifying x + -1.538461539 = -1.926919239 Reorder the terms: -1.538461539 + x = -1.926919239 Solving -1.538461539 + x = -1.926919239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.538461539' to each side of the equation. -1.538461539 + 1.538461539 + x = -1.926919239 + 1.538461539 Combine like terms: -1.538461539 + 1.538461539 = 0.000000000 0.000000000 + x = -1.926919239 + 1.538461539 x = -1.926919239 + 1.538461539 Combine like terms: -1.926919239 + 1.538461539 = -0.3884577 x = -0.3884577 Simplifying x = -0.3884577Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.465380778, -0.3884577}
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