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Simplifying 25x2 + -36x + 12 = 0 Reorder the terms: 12 + -36x + 25x2 = 0 Solving 12 + -36x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.48 + -1.44x + x2 = 0 Move the constant term to the right: Add '-0.48' to each side of the equation. 0.48 + -1.44x + -0.48 + x2 = 0 + -0.48 Reorder the terms: 0.48 + -0.48 + -1.44x + x2 = 0 + -0.48 Combine like terms: 0.48 + -0.48 = 0.00 0.00 + -1.44x + x2 = 0 + -0.48 -1.44x + x2 = 0 + -0.48 Combine like terms: 0 + -0.48 = -0.48 -1.44x + x2 = -0.48 The x term is -1.44x. Take half its coefficient (-0.72). Square it (0.5184) and add it to both sides. Add '0.5184' to each side of the equation. -1.44x + 0.5184 + x2 = -0.48 + 0.5184 Reorder the terms: 0.5184 + -1.44x + x2 = -0.48 + 0.5184 Combine like terms: -0.48 + 0.5184 = 0.0384 0.5184 + -1.44x + x2 = 0.0384 Factor a perfect square on the left side: (x + -0.72)(x + -0.72) = 0.0384 Calculate the square root of the right side: 0.195959179 Break this problem into two subproblems by setting (x + -0.72) equal to 0.195959179 and -0.195959179.Subproblem 1
x + -0.72 = 0.195959179 Simplifying x + -0.72 = 0.195959179 Reorder the terms: -0.72 + x = 0.195959179 Solving -0.72 + x = 0.195959179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.72' to each side of the equation. -0.72 + 0.72 + x = 0.195959179 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + x = 0.195959179 + 0.72 x = 0.195959179 + 0.72 Combine like terms: 0.195959179 + 0.72 = 0.915959179 x = 0.915959179 Simplifying x = 0.915959179Subproblem 2
x + -0.72 = -0.195959179 Simplifying x + -0.72 = -0.195959179 Reorder the terms: -0.72 + x = -0.195959179 Solving -0.72 + x = -0.195959179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.72' to each side of the equation. -0.72 + 0.72 + x = -0.195959179 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + x = -0.195959179 + 0.72 x = -0.195959179 + 0.72 Combine like terms: -0.195959179 + 0.72 = 0.524040821 x = 0.524040821 Simplifying x = 0.524040821Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.915959179, 0.524040821}
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