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Simplifying 6x2 + -12x + 5 = 0 Reorder the terms: 5 + -12x + 6x2 = 0 Solving 5 + -12x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -2x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -2x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -2x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.8333333333 -2x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -2x + x2 = -0.8333333333 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 = -0.8333333333 + 1 Reorder the terms: 1 + -2x + x2 = -0.8333333333 + 1 Combine like terms: -0.8333333333 + 1 = 0.1666666667 1 + -2x + x2 = 0.1666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.1666666667 Calculate the square root of the right side: 0.408248291 Break this problem into two subproblems by setting (x + -1) equal to 0.408248291 and -0.408248291.Subproblem 1
x + -1 = 0.408248291 Simplifying x + -1 = 0.408248291 Reorder the terms: -1 + x = 0.408248291 Solving -1 + x = 0.408248291 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 = 0.408248291 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.408248291 + 1 x = 0.408248291 + 1 Combine like terms: 0.408248291 + 1 = 1.408248291 x = 1.408248291 Simplifying x = 1.408248291Subproblem 2
x + -1 = -0.408248291 Simplifying x + -1 = -0.408248291 Reorder the terms: -1 + x = -0.408248291 Solving -1 + x = -0.408248291 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 = -0.408248291 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.408248291 + 1 x = -0.408248291 + 1 Combine like terms: -0.408248291 + 1 = 0.591751709 x = 0.591751709 Simplifying x = 0.591751709Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.408248291, 0.591751709}
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