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Simplifying 4x2 + -42x + 13 = 0 Reorder the terms: 13 + -42x + 4x2 = 0 Solving 13 + -42x + 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'. 3.25 + -10.5x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -10.5x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -10.5x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -10.5x + x2 = 0 + -3.25 -10.5x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -10.5x + x2 = -3.25 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = -3.25 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -3.25 + 27.5625 Combine like terms: -3.25 + 27.5625 = 24.3125 27.5625 + -10.5x + x2 = 24.3125 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 24.3125 Calculate the square root of the right side: 4.930770731 Break this problem into two subproblems by setting (x + -5.25) equal to 4.930770731 and -4.930770731.Subproblem 1
x + -5.25 = 4.930770731 Simplifying x + -5.25 = 4.930770731 Reorder the terms: -5.25 + x = 4.930770731 Solving -5.25 + x = 4.930770731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 4.930770731 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.930770731 + 5.25 x = 4.930770731 + 5.25 Combine like terms: 4.930770731 + 5.25 = 10.180770731 x = 10.180770731 Simplifying x = 10.180770731Subproblem 2
x + -5.25 = -4.930770731 Simplifying x + -5.25 = -4.930770731 Reorder the terms: -5.25 + x = -4.930770731 Solving -5.25 + x = -4.930770731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -4.930770731 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.930770731 + 5.25 x = -4.930770731 + 5.25 Combine like terms: -4.930770731 + 5.25 = 0.319229269 x = 0.319229269 Simplifying x = 0.319229269Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.180770731, 0.319229269}
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