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Simplifying -0.9375 + -9.375x + -3x2 + 4.5625x2 = 0 Combine like terms: -3x2 + 4.5625x2 = 1.5625x2 -0.9375 + -9.375x + 1.5625x2 = 0 Solving -0.9375 + -9.375x + 1.5625x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5625 the coefficient of the squared term: Divide each side by '1.5625'. -0.6 + -6x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -6x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -6x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -6x + x2 = 0 + 0.6 -6x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -6x + x2 = 0.6 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 0.6 + 9 Reorder the terms: 9 + -6x + x2 = 0.6 + 9 Combine like terms: 0.6 + 9 = 9.6 9 + -6x + x2 = 9.6 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.6 Calculate the square root of the right side: 3.098386677 Break this problem into two subproblems by setting (x + -3) equal to 3.098386677 and -3.098386677.Subproblem 1
x + -3 = 3.098386677 Simplifying x + -3 = 3.098386677 Reorder the terms: -3 + x = 3.098386677 Solving -3 + x = 3.098386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.098386677 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.098386677 + 3 x = 3.098386677 + 3 Combine like terms: 3.098386677 + 3 = 6.098386677 x = 6.098386677 Simplifying x = 6.098386677Subproblem 2
x + -3 = -3.098386677 Simplifying x + -3 = -3.098386677 Reorder the terms: -3 + x = -3.098386677 Solving -3 + x = -3.098386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.098386677 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.098386677 + 3 x = -3.098386677 + 3 Combine like terms: -3.098386677 + 3 = -0.098386677 x = -0.098386677 Simplifying x = -0.098386677Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.098386677, -0.098386677}
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