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Simplifying 4x2 + -6x + 0.69 = 0 Reorder the terms: 0.69 + -6x + 4x2 = 0 Solving 0.69 + -6x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.1725 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.1725' to each side of the equation. 0.1725 + -1.5x + -0.1725 + x2 = 0 + -0.1725 Reorder the terms: 0.1725 + -0.1725 + -1.5x + x2 = 0 + -0.1725 Combine like terms: 0.1725 + -0.1725 = 0.0000 0.0000 + -1.5x + x2 = 0 + -0.1725 -1.5x + x2 = 0 + -0.1725 Combine like terms: 0 + -0.1725 = -0.1725 -1.5x + x2 = -0.1725 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.1725 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.1725 + 0.5625 Combine like terms: -0.1725 + 0.5625 = 0.39 0.5625 + -1.5x + x2 = 0.39 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.39 Calculate the square root of the right side: 0.6244998 Break this problem into two subproblems by setting (x + -0.75) equal to 0.6244998 and -0.6244998.Subproblem 1
x + -0.75 = 0.6244998 Simplifying x + -0.75 = 0.6244998 Reorder the terms: -0.75 + x = 0.6244998 Solving -0.75 + x = 0.6244998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.6244998 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.6244998 + 0.75 x = 0.6244998 + 0.75 Combine like terms: 0.6244998 + 0.75 = 1.3744998 x = 1.3744998 Simplifying x = 1.3744998Subproblem 2
x + -0.75 = -0.6244998 Simplifying x + -0.75 = -0.6244998 Reorder the terms: -0.75 + x = -0.6244998 Solving -0.75 + x = -0.6244998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.6244998 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.6244998 + 0.75 x = -0.6244998 + 0.75 Combine like terms: -0.6244998 + 0.75 = 0.1255002 x = 0.1255002 Simplifying x = 0.1255002Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3744998, 0.1255002}
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