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Simplifying 15x2 + -30x + 13 = 0 Reorder the terms: 13 + -30x + 15x2 = 0 Solving 13 + -30x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.8666666667 + -2x + x2 = 0 Move the constant term to the right: Add '-0.8666666667' to each side of the equation. 0.8666666667 + -2x + -0.8666666667 + x2 = 0 + -0.8666666667 Reorder the terms: 0.8666666667 + -0.8666666667 + -2x + x2 = 0 + -0.8666666667 Combine like terms: 0.8666666667 + -0.8666666667 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.8666666667 -2x + x2 = 0 + -0.8666666667 Combine like terms: 0 + -0.8666666667 = -0.8666666667 -2x + x2 = -0.8666666667 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 = -0.8666666667 + 1 Reorder the terms: 1 + -2x + x2 = -0.8666666667 + 1 Combine like terms: -0.8666666667 + 1 = 0.1333333333 1 + -2x + x2 = 0.1333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.1333333333 Calculate the square root of the right side: 0.365148372 Break this problem into two subproblems by setting (x + -1) equal to 0.365148372 and -0.365148372.Subproblem 1
x + -1 = 0.365148372 Simplifying x + -1 = 0.365148372 Reorder the terms: -1 + x = 0.365148372 Solving -1 + x = 0.365148372 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 = 0.365148372 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.365148372 + 1 x = 0.365148372 + 1 Combine like terms: 0.365148372 + 1 = 1.365148372 x = 1.365148372 Simplifying x = 1.365148372Subproblem 2
x + -1 = -0.365148372 Simplifying x + -1 = -0.365148372 Reorder the terms: -1 + x = -0.365148372 Solving -1 + x = -0.365148372 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 = -0.365148372 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.365148372 + 1 x = -0.365148372 + 1 Combine like terms: -0.365148372 + 1 = 0.634851628 x = 0.634851628 Simplifying x = 0.634851628Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.365148372, 0.634851628}
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