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Simplifying 4x2 + -50x + 51 = 0 Reorder the terms: 51 + -50x + 4x2 = 0 Solving 51 + -50x + 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'. 12.75 + -12.5x + x2 = 0 Move the constant term to the right: Add '-12.75' to each side of the equation. 12.75 + -12.5x + -12.75 + x2 = 0 + -12.75 Reorder the terms: 12.75 + -12.75 + -12.5x + x2 = 0 + -12.75 Combine like terms: 12.75 + -12.75 = 0.00 0.00 + -12.5x + x2 = 0 + -12.75 -12.5x + x2 = 0 + -12.75 Combine like terms: 0 + -12.75 = -12.75 -12.5x + x2 = -12.75 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -12.75 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -12.75 + 39.0625 Combine like terms: -12.75 + 39.0625 = 26.3125 39.0625 + -12.5x + x2 = 26.3125 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 26.3125 Calculate the square root of the right side: 5.129571132 Break this problem into two subproblems by setting (x + -6.25) equal to 5.129571132 and -5.129571132.Subproblem 1
x + -6.25 = 5.129571132 Simplifying x + -6.25 = 5.129571132 Reorder the terms: -6.25 + x = 5.129571132 Solving -6.25 + x = 5.129571132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 5.129571132 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 5.129571132 + 6.25 x = 5.129571132 + 6.25 Combine like terms: 5.129571132 + 6.25 = 11.379571132 x = 11.379571132 Simplifying x = 11.379571132Subproblem 2
x + -6.25 = -5.129571132 Simplifying x + -6.25 = -5.129571132 Reorder the terms: -6.25 + x = -5.129571132 Solving -6.25 + x = -5.129571132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -5.129571132 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -5.129571132 + 6.25 x = -5.129571132 + 6.25 Combine like terms: -5.129571132 + 6.25 = 1.120428868 x = 1.120428868 Simplifying x = 1.120428868Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.379571132, 1.120428868}
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