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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 = 30.640625 40.640625 + -12.75x + x2 = 30.640625 Factor a perfect square on the left side: (x + -6.375)(x + -6.375) = 30.640625 Calculate the square root of the right side: 5.535397456 Break this problem into two subproblems by setting (x + -6.375) equal to 5.535397456 and -5.535397456.Subproblem 1
x + -6.375 = 5.535397456 Simplifying x + -6.375 = 5.535397456 Reorder the terms: -6.375 + x = 5.535397456 Solving -6.375 + x = 5.535397456 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 = 5.535397456 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + x = 5.535397456 + 6.375 x = 5.535397456 + 6.375 Combine like terms: 5.535397456 + 6.375 = 11.910397456 x = 11.910397456 Simplifying x = 11.910397456Subproblem 2
x + -6.375 = -5.535397456 Simplifying x + -6.375 = -5.535397456 Reorder the terms: -6.375 + x = -5.535397456 Solving -6.375 + x = -5.535397456 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 = -5.535397456 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + x = -5.535397456 + 6.375 x = -5.535397456 + 6.375 Combine like terms: -5.535397456 + 6.375 = 0.839602544 x = 0.839602544 Simplifying x = 0.839602544Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.910397456, 0.839602544}
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