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Simplifying 5x(5x) + -26x + 5 = 0 Remove parenthesis around (5x) 5x * 5x + -26x + 5 = 0 Reorder the terms for easier multiplication: 5 * 5x * x + -26x + 5 = 0 Multiply 5 * 5 25x * x + -26x + 5 = 0 Multiply x * x 25x2 + -26x + 5 = 0 Reorder the terms: 5 + -26x + 25x2 = 0 Solving 5 + -26x + 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'. 0.2 + -1.04x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.04x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.04x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.04x + x2 = 0 + -0.2 -1.04x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.04x + x2 = -0.2 The x term is -1.04x. Take half its coefficient (-0.52). Square it (0.2704) and add it to both sides. Add '0.2704' to each side of the equation. -1.04x + 0.2704 + x2 = -0.2 + 0.2704 Reorder the terms: 0.2704 + -1.04x + x2 = -0.2 + 0.2704 Combine like terms: -0.2 + 0.2704 = 0.0704 0.2704 + -1.04x + x2 = 0.0704 Factor a perfect square on the left side: (x + -0.52)(x + -0.52) = 0.0704 Calculate the square root of the right side: 0.265329983 Break this problem into two subproblems by setting (x + -0.52) equal to 0.265329983 and -0.265329983.Subproblem 1
x + -0.52 = 0.265329983 Simplifying x + -0.52 = 0.265329983 Reorder the terms: -0.52 + x = 0.265329983 Solving -0.52 + x = 0.265329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.52' to each side of the equation. -0.52 + 0.52 + x = 0.265329983 + 0.52 Combine like terms: -0.52 + 0.52 = 0.00 0.00 + x = 0.265329983 + 0.52 x = 0.265329983 + 0.52 Combine like terms: 0.265329983 + 0.52 = 0.785329983 x = 0.785329983 Simplifying x = 0.785329983Subproblem 2
x + -0.52 = -0.265329983 Simplifying x + -0.52 = -0.265329983 Reorder the terms: -0.52 + x = -0.265329983 Solving -0.52 + x = -0.265329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.52' to each side of the equation. -0.52 + 0.52 + x = -0.265329983 + 0.52 Combine like terms: -0.52 + 0.52 = 0.00 0.00 + x = -0.265329983 + 0.52 x = -0.265329983 + 0.52 Combine like terms: -0.265329983 + 0.52 = 0.254670017 x = 0.254670017 Simplifying x = 0.254670017Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.785329983, 0.254670017}
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