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Simplifying 4x2 + -51x = 40 Reorder the terms: -51x + 4x2 = 40 Solving -51x + 4x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + -51x + 4x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -51x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10 + -12.75x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -12.75x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -12.75x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -12.75x + x2 = 0 + 10 -12.75x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -12.75x + x2 = 10 The x term is -12.75x. Take half its coefficient (-6.375). Square it (40.640625) and add it to both sides. Add '40.640625' to each side of the equation. -12.75x + 40.640625 + x2 = 10 + 40.640625 Reorder the terms: 40.640625 + -12.75x + x2 = 10 + 40.640625 Combine like terms: 10 + 40.640625 = 50.640625 40.640625 + -12.75x + x2 = 50.640625 Factor a perfect square on the left side: (x + -6.375)(x + -6.375) = 50.640625 Calculate the square root of the right side: 7.116222664 Break this problem into two subproblems by setting (x + -6.375) equal to 7.116222664 and -7.116222664.Subproblem 1
x + -6.375 = 7.116222664 Simplifying x + -6.375 = 7.116222664 Reorder the terms: -6.375 + x = 7.116222664 Solving -6.375 + x = 7.116222664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.375' to each side of the equation. -6.375 + 6.375 + x = 7.116222664 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + x = 7.116222664 + 6.375 x = 7.116222664 + 6.375 Combine like terms: 7.116222664 + 6.375 = 13.491222664 x = 13.491222664 Simplifying x = 13.491222664Subproblem 2
x + -6.375 = -7.116222664 Simplifying x + -6.375 = -7.116222664 Reorder the terms: -6.375 + x = -7.116222664 Solving -6.375 + x = -7.116222664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.375' to each side of the equation. -6.375 + 6.375 + x = -7.116222664 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + x = -7.116222664 + 6.375 x = -7.116222664 + 6.375 Combine like terms: -7.116222664 + 6.375 = -0.741222664 x = -0.741222664 Simplifying x = -0.741222664Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.491222664, -0.741222664}
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