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Simplifying 12x2 + -24x + 7.8 = 0 Reorder the terms: 7.8 + -24x + 12x2 = 0 Solving 7.8 + -24x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.65 + -2x + x2 = 0 Move the constant term to the right: Add '-0.65' to each side of the equation. 0.65 + -2x + -0.65 + x2 = 0 + -0.65 Reorder the terms: 0.65 + -0.65 + -2x + x2 = 0 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + -2x + x2 = 0 + -0.65 -2x + x2 = 0 + -0.65 Combine like terms: 0 + -0.65 = -0.65 -2x + x2 = -0.65 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.65 + 1 Reorder the terms: 1 + -2x + x2 = -0.65 + 1 Combine like terms: -0.65 + 1 = 0.35 1 + -2x + x2 = 0.35 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.35 Calculate the square root of the right side: 0.591607978 Break this problem into two subproblems by setting (x + -1) equal to 0.591607978 and -0.591607978.Subproblem 1
x + -1 = 0.591607978 Simplifying x + -1 = 0.591607978 Reorder the terms: -1 + x = 0.591607978 Solving -1 + x = 0.591607978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.591607978 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.591607978 + 1 x = 0.591607978 + 1 Combine like terms: 0.591607978 + 1 = 1.591607978 x = 1.591607978 Simplifying x = 1.591607978Subproblem 2
x + -1 = -0.591607978 Simplifying x + -1 = -0.591607978 Reorder the terms: -1 + x = -0.591607978 Solving -1 + x = -0.591607978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.591607978 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.591607978 + 1 x = -0.591607978 + 1 Combine like terms: -0.591607978 + 1 = 0.408392022 x = 0.408392022 Simplifying x = 0.408392022Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.591607978, 0.408392022}
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